I find that in pauses between action and dialogue, my character's thoughts really don't seem realistic. I think I tend to mostly write questions for my character's thoughts. I also don't know if I'm biased because I'm the author when I read something I wrote for my character's thought process, and if that might change how I perceive how realistic it is. How can I improve?
One thing that has helped me tremendously with making thought processes more realistic is to read the parts in question to another person, then stop at the relevant points and make them write down what they would've thought in the situation of the character. As an author, you suffer from "author's blindness" - due to the fact that you know where things are heading - at least roughly - you don't approach situations naturally.
Therefore, whenever I have to write a section with realistic character thoughts, I read that section to my girlfriend or my brother (the two people around me most interested in my writing) and ask them what they would've thought if they had been the situation of the character.
(On a side note: I usually also try to match the gender, so when it's a female character, I ask my girlfriend for advice, when it's a male character, I ask my brother for advice, because I think that many authors fall into the trap of thinking that men and women think exactly alike, while in reality, they approach situations very differently, which often results in male authors writing unrealistic female characters and female authors writing unrealistic male characters.)
my character's thoughts really don't seem realistic.
I am struggling to guess what the issue might be. 'Not realistic' doesn't describe a specific problem, or point to a solution.
Who is this character? Are they curious but innocent? Are they experienced and wise? Are they biased and impulsive? Are they social-climbing, or biting their tongue to not say what they actually believe? Are this person's internal thoughts any different from their actions and dialog?
A James Bond-type doesn't need internal debates because he gets to react to the plot on any impulse, including sexual assault and killing people. Philip Marlowe doesn't think-through a mystery with his grey cells, his method is to provoke suspects and see what they reveal – Marlowe's famous internal monologues are a stream of sensual descriptions that are more style than character, making him almost an artful narrator and witness of the seedy circumstances rather than a pro-active protagonist who is trying to make things 'right'.
In contrast, an enslaved prisoner, a domestic servant, a low-ranked soldier, a repressed wife or abused child don't get to say or do anything that reflects their actual beliefs, everything must be internal, they cannot openly protest the plot or their higher-ups without consequences. These characters must show some contradiction in what they think and what they do.
Does this character evolve in some way that can't be shown through their behavior? There may not be enough internal-conflict to sustain a character monologue. If you have to force it, it might not be necessary.
I tend to mostly write questions for my character's thoughts.
This suggests the MC's head is being used by the author to re-tell the main plot-points (again I have to read-between-the-lines of your question). I am imagining the MC internally asking questions the reader is meant to ask, but not getting any answer and not coming to any conclusion of their own.
The reason to have a character think something is (generally) so they can be wrong about it. What the character assumes is not what has actually happened. When they react to the plot, they generate new complications by doing the wrong thing, but it was justifiable at the time.
Your character should not just be asking open-ended questions. They need to be coming up with answers which inform their behavior which feeds back into the plot – it just so happens they've jumped to the wrong conclusion so their actions bring more conflict. This is why a character's flaws have become such an important writing tool, they find themselves in a hole and spend the first half of the story digging themselves in deeper.
A character who 'just asks questions' isn't playing an active role in finding a solution, they are passive.
The acronym JAQ ('just asking questions') is a label for a disingenuous trolling technique: someone asks a lot of (mis)leading questions and then shrugs off the ensuing answers by saying they're 'just asking questions'. In most narratives, as in real life, the answers are usually painfully obvious. It doesn't take long to realize the troll is 'JAQ-ing off' to use the internet term, because they must actively avoid using any logic at all to suspend a question indefinitely.
Occam's razor provides very simple answers after a short think. Your reader may lose empathy for an MC who seems too stupid to come up with the most obvious answer to their own questions. Therefore, the MC should come to a conclusion, and that conclusion should be wrong because of their limited knowledge and POV. An MC's unacknowledged biases may also be strong enough to allow them to ignore Occam's razor.
Trends in streaming TV often use 'mystery bait' to string the audience along to keep watching. These elements are designed to be unanswerable and open-ended. They are signaled as cliff-hangers and 'strange' plot points, but do not have a real conclusion. I'm assuming this is not the sort of question your MC is asking themselves.
A professional detective, or a clever psychologist, may have the training to suspend logical conclusions because they know the specific answer is not as important as understanding the question itself. The question is a MacGuffin that something is not right, and is typically lampshaded either by another character's too-quick conclusions, or by making the question nag at the detective. It's a mystery because it is a mystery, MC and reader are put on the same page, although these MacGuffin clues can feel contrived by serving the plot.
Coming-of-age protagonists do not understand adult-mysteries, but they may notice something and ask the wrong questions – an innocent jumping to conclusions or a social-etiquite faux pas. The reader will be several steps ahead of these characters and it's usually not necessary for them to actually learn the answer for the narrative to work – therefore maybe not necessary for the MC to have a solid answer even if the reader can make a logical conclusion. The fact the MC learns that certain things are outside their knowledge is character growth.
In all of these instances, the author is putting the question in the MC's mouth for a reason. There needs to be a payoff or it's just a shaggy dog story.
Maybe your MC is forcing an internal monologue to fill the page? If they keep asking questions but not arriving at conclusions, this sounds like 'filler'. Perhaps you need a separate narrator, or a stronger narrative voice.
The strongest 3rd-person voice is Free Indirect Speech, a technique used by Jane Austen for stating internal opinions from any character as facts, without cumbersome "She thought to herself" connecting text.
Austen allowed her characters to be wrong about everything, having the strongest opinions and prejudices against the very things they need most. Their dogma feeds the plot, generating extra conflict with the lesson life throws at them. Austen's novels follow women in Regency England, a world with insane levels of social etiquette that prevented the heroines (anyone really) from speaking their honest minds, yet characters use emphatic self-serving logic, characters straight-up lie through entire books, and huge chunks of the extended story are told 2nd-hand through cagey, polite letters.
Counterintuitively, Austen developed Free Indirect Speech as her narrative voice. She mostly follows one MC with a respectful 3rd-person distance, but any character can blurt out snarky, honest-but-raw thoughts as if the reader had a glimpse into their impulsive mind for a brief (usually unflattering) moment. The MC meanwhile warps the world to match her own emotional state – when she is unhappy the objects around her reflect it. Despite the logistical constraints of her protagonists, Austen invents the free-est narrative voice. In a world where no one can speak the truth and protagonists have extreme biases, Austen's narrator somehow reveals all the truths, adding layers of dimension to reserved characters.
You might try reading some of Virginia Woolf's stories, for example To The Lighthouse or Mrs Dalloway. She is famous for using the "stream of consciousness" style where the majority of the story focuses on a character's inner thoughts. There are lists of other writers famous for this style you can find online. You may not care for their stories but reading them might help you learn their techniques for how to write a characters thoughts.
OK. This will be my very first answer here, so tame your judgments!
I just read wetcircuit's comprehensive and stimulating answer.
To be honest, it was the last part that I found truly engaging.
MC stereotypes like high-rolling agents, hyper-rational detectives, or forlorn victims of social injustice don't really belong to (or fit in, perhaps) my "palette" of characters.
And I'm not really into plot technicalities either. I acknowledge that they do serve a purpose, but in my humble opinion, that's not the main purpose of either writing or reading (both of which are, ultimately, very private activities, so one's humble opinion does have a bearing.)
But when wetcircuit comes to Jane Austen, things start to get seriously interesting:
Austen allowed her characters to be wrong about everything, having the strongest opinions and prejudices against the very things they need most.
Allow me to expand on that in a somewhat different direction:
Somewhere in The Art of the Novel, Milan Kundera says something along the lines of how decisive it is to be able to enforce your characters' egos upon the reader. (Not sure I still got the book, and even if I have it, I'd have to translate the [translated] excerpt from Greek, so you will have to take my word for the quote's validity.)
Personally, I have found this stance to be very inspiring. When it comes to inner dialogues, for example, they don't necessarily need to advance the "plot". They can be mere subtle egocentric observations, while looking at the bathroom mirror ("I'm growing bald...") or strolling through the forest ("This is what being alive should feel like...")
I find that a character's moments of solitude can serve as a good starting point to develop their ego: How do they relate to their immediate surroundings? How important do they think they are? Once you sort this out, they start acquiring their own unique style as commentators of whatever's happening around them, and subsequently, this inner commentary starts following them around through the story, sometimes expressed (dialogue), sometimes implied (thoughts).
It's been many years since I read Sartre's Nausea, but what I remember of it (and I remember it with appreciation) is an entire novel made of solemn associations about a man's immediate surroundings, be it interior or exterior, people or still life. The consistency in the "tone of thought" is basically what holds the book together.
Lastly, another intriguing essay-like book in this regard is Turgenev's Hamlet and Don Quixote, where the Russian sheds his own cautious light upon the two iconic characters, presenting them as each other's antipode: Hamlet, the restless doubter, perpetually tormented by knowledge's inherent limitations versus Don Quixote, the happy believer, indulging in his own delusions, oblivious of how evident their foolishness may be.
Somewhere between the two, you'll probably find room for your own characters, too.