For example, let’s say the main plot is that the characters are on a quest to go find something. Can an author spend three scenes in a row detailing what happens on their journey there, even if the only way the plot is moving forwards is by the implication that they’re moving in that direction? What if they spend three nights (and three scenes) at the same pitstop, but the scenes greatly develop the relationship between two important characters?
If you are talking about chapters which have some significant plot development but the focus of the chapter is on the characters' interaction, that's perfectly okay.
However, if the the advancement is just that the characters are moving toward a particular location, I have always found this is not a good idea. My main critiquing group refers to this (not fondly) as the "road trip syndrome". Just recently when we were critiquing someone's chapter, I was reminded of that scene in Poltergeist where the mom is walking down the hall and as she walks, the hallway stretches out, and the longer she walks the farther away the destination seems, and she breaks into a run and suddenly, snap, she arrives.
We had listened to four chapters of traveling to get to the city. There were interesting things that happened and there was good character development, but, as one fellow critiquer had remarked of the previous chapter, "good lord, when are they going to get there?"
Being a character focused writer myself, one thing I know I have to watch out for is the fact that although my characters are fascinating to me, they aren't always going to be to other people. Too heavy on the character development, and plot-focused readers get impatient.
I have always heard from critiquers and teachers and panelists at writing cons that it is a hard rule that each chapter must advance the plot in some way, and it can't be the same way. Thus, you can have a chapter of "they travel to the city" but if it stretches out for more than a single chapter you have to include other plot developments.
That doesn't mean you can't spend time for character development, or that you can't have chapters that focus on character development, but that development needs to come with plot advancement. It doesn't necessarily have to cause the plot development, but it needs to be mingled with it.
For example, say you have two characters and you want to have them get to know each other, and have an incident that changes their relationship. (BTW, I am assuming this is not a romance. If it is, then the romance is the plot...) Perhaps their interaction is triggered by a discovery that one of them makes which is part of the mystery that they are trying to solve.
If you have a strong interest in your characters, then all you need to do is drop "plot seeds" into your story; items that advance the plot by a step, and then have your characters' personalities react to that. Remember, characters are best developed through interaction with external forces.
Here's a rule of thumb that I have found useful. When you get done with a character driven chapter ask yourself "what action was taken by a character in this chapter that will have obvious consequences on the plot?" If the answer is nothing, try to find something that will, and weave it into the chapter.
A good plot is like a box of chocolates, whoops, I mean a box of dominoes. You set them up so that the first one needs a push (whatever triggering incident or condition launches the story) and after that, the fall of each domino causes the next to fall. If your story goes too long without a major plot point it's like two dominoes which are too far apart and even if your characters are fascinating it can feel like your engine is racing but the car isn't in gear.
What if they spend three nights (and three scenes) at the same pitstop, but the scenes greatly develop the relationship between two important characters?
Yes, that would be fine, with one caveat that applies to every scene of your story: You still need some kind of tension, some reason for the reader to be wondering what is going to happen next, that is "coming up" in whatever you write.
The tension can be about the plot or problem they are facing, but it can also be about their relationship. Romance is one obvious way to introduce tension, but there are relationships other than romance, that need to evolve from Point A to Point B: e.g. a father that has just finished ten years in prison, with his teen daughter he hasn't seen since she was six. Or two former friends are forced together, one of whom betrayed the other for money.
Like Romance, these are "will they or won't they" relationships with a less certain outcome: Will the daughter forgive her criminal father? Will the former friends reconcile, or will one betray the other?
You have to make this relationship development interesting for the reader, keep them anticipating and wanting to turn pages to hear what happens next, and they won't even notice the plot isn't advancing.
They start wondering when you will finish whenever the story loses tension, and it doesn't matter what kind of scene it was. The scene needs tension, conflict, an uncertain future. If it is predictable without surprises, shorten it to a description as much as possible, which may be to zero (cut the scene altogether). Identify the kind of change you are trying to show in that scene. Where is Point A, and What is Point B? This is true whether it is a relationship, the plot, the setting, new knowledge or clues discovered. There is inherent tension in that change, so you can sharpen your focus on a scene designed to show the evolution from A to B.
Readers keep turning pages to see how something turns out, but they can get tired of that if what they are waiting for seems interminably delayed. There is not a lot of patience. You need a layered approach to this; they should want to see how a scene turns out; simultaneously wanting to see how the chapter turns out, how the Act turns out (whether they know what an Act is or not), and how the story turns out. The layered approach also means you need to keep introducing the steps on this path, one scene with tension begets the next scene with tension.
For example, you have them on a trip: The reason for this trip is a source of tension; the reader wants to know how THAT will turn out. That is something they can talk about, developing their relationship, and perhaps come up with decisions or ideas that become new points of tension: Will those work out?
How characters think, learn, succeed or fail is the source of these new elements of tension.
You might want to break up the three scenes with something else, but generally speaking, yes, it's okay to focus on character development even if there isn't a ton of plot movement. Maybe add in a short scene which advances the antagonist's part of the plot arc?
Readers do want to root for your characters. We want to care. Developing the characters and helping us understand why we should care is a good use of pages.
As a generality, stories are about people and how their interactions with each other change them. Adding richness to your characters' journey, even if those aspects do not affect their arc, can be just that: richness.
(If you need to think of this mechanically, this can be a tool to break characters out of being one-dimensional tropes. Just take heed of the points raised by the other answers: always be mindful of how these scenes effect the pace.)