Personally, I go by the number of scenes they are in. Basically:
If they are in one scene, and neither mentioned or seen after that, they are one dimensional. They may not even have a name. Now, one-dimensional doesn't mean I can't describe them. My MC may see the young waitress flirting with the young guy at the counter. The waitress may be funny, or when my MC orders may grimace as if in pain and shake her head, warning the MC away from a dish. One dimensional does not mean she cannot be humanized, it means she exists only in this moment, as a waitress, and we don't delve into her past or future.
If they are in one scene and either appear or are referred to in a later scene, they are two-dimensional; meaning I will make them (in their first appearance) somehow memorable or interesting to the MC. I don't know how; that will require imagination. At minimum they will have a name the MC will remember. Preferably they will be connected to the MC's quest in some way. And probably they will have some past (i.e. something they have been doing, or a story of what they have been through) and/or some future (plans, destination, mission, whatever). I want the reader to remember the character for their later reference or appearance. But they don't need a full-blown history, emotions, etc. Two-dimensional is like a cardboard cutout, which can be a recognizable and memorable character, but we don't need a deep background for this character.
If they appear (or are referenced) in three or more distinct scenes, I want them to be three dimensional characters. I make exceptions to this rule if their appearances are all scenes in a row: If the character is not going to be seen or referenced after those scenes, they likely remain a 2-d character. I expect the reader to remember them from the previous scene. For example, this might be true of a guard the MC is bribing, or an office worker she is paying for inside information.
Exceptions: I agree with your (OP) sentiment about showing ups and downs in a person's life to flesh them out, showing them in various circumstances. If there just isn't room in the narrative to cram that stuff in for a character, lower the dimensionality of the character, regardless of how often they appear. The 1-2-3 above is more of a guideline to tell you when you should be thinking about upping the dimensionality, or when the reader might be dissatisfied with your portrayal of character.
Readers do not mind walk-ons, IRL there can be literally hundreds of silent walk-on characters we pass by without a thought while navigating the city for business or even just going to lunch, and in a normal day we may speak with a dozen people for the first and only time in our lives. They don't mind 2-D characters either; don't get bogged down in them. We've all had classmates and office-mates we knew for years, and had many conversations with, without "getting to know them" at any more than a superficial level.
Going by "feel" is not a bad way of doing it, the only thing to guard against is pointless exposition about a wonderful character that does not do anything for your plot or entertainment value or MC character growth. Make sure you are not writing just to entertain yourself with making up an interesting character that doesn't go on to actually do anything important. You need to entertain the reader, and stalling the story to digress on such a character is going to confuse them, not entertain them.
I can engineer spending four pages with my MC and the waitress in conversation, fleshing out the waitress's life and making her feel real. But if I do that the reader expects the waitress to appear again, to play some role. If I walk away from her and she never appears again the reader wonders what the hell that was all about.
So the more general rule is this: When you start fleshing out a character, you have begun a character arc for them, at least a partial arc. So make sure they have some role in the MC's future and in how the story resolves. How much arc you describe for them should be proportional to the influence of that role. No influence=walk on character. Some influence = 2-D character. Big influence = 3-D character.