I am sorry that I do not have an exact answer to the question on the title.
But here is the core of the question
I'm looking more for general principles and ideas.
So here are my two cents:
1. Focal length and aperture
Yes, I know. I started with something is not controlled by color grading, but it needs to be said.
2. Color correction
This is the first step, define what was the white balance and exposure and make them coherent.
On programs like Resolve, one node should be for temperature correction and another for exposure.
Here is probably the first manipulation we need to make, Do we have a correct exposure of the shadows? Do we need to actually change a curve to show detail?
This is, for now, more than a creative manipulation but about Information. Does the shadowy part of the face of an actor need to be viewed clearly? Does he have a scar that does not show good enough and needs to be brightened?
3. Dynamic range, overall contrast
We are limited by the capabilities of the camera, but we can work around this, using illumination techniques, both positive and negative illumination.
Positive illumination is where you add light on dark zones where you have little light. One case is where you have a sunset behind the subject and you add a reflector to reduce the contrast.
Negative illumination is reducing the light of the bright part, either controlled by a filter or by shutter speed or something.
But when referring to color grading this element is more noticeable on one particular characteristic: Contrast.
So, you can play with the contrast. Sometimes reducing the blackness makes the image a bit more "filmish" or with a film substrate.
It is funny that you mentioned "Still Photography" because I will reference a post I made on that forum, no spam intended :o) https://photo.stackexchange.com/questions/110840/whats-the-biggest-difference-between-these-two-photos-of-large-animals/110884#110884
See how reducing the contrast, by graying the black point, make the image look with a higher dynamic range... This is funny because it is the opposite.
4. Middle tones
You probably want to maintain the middle tones accurate to the color corrections you made in the first place. But this rule can be broken of course. See point 7.
Play with the saturation.
5. Color on the shadows
So we actually need to start creative somewhere. A typical teal and orange look starts here, change the temperature of the shadows. Normally a shadow is a bit cooler than the highlights.
6. Now the light
Change the temperature on the highlights, blow them on a desert scenario, gray them and cool them on a moody swamp.
7. Middle tones again
To change the overall mood, you know the typical matrix example with green tones overall...
8. Forget everything
I or somebody say and play.
9. A side note about "cliches"
Especially for region-based, or country-based color recipes, this is a country that has some deserts... Oh, All the countries should be painted orange!
The US has some pretty big deserts, and you should not grade all movies orange.
The UK, London has some foggy days, not every scene should be desaturated... (or should they? Lol, sorry... I could not resist)
Some red alert scenario... Dam, we need the best light to work on a red alert scenario, not a red light!
Sometimes the cliche is annoying if overdone. Forget cliches, or use them, it is your call.