To answer your questions:
-The door ajar light does work
-Water temp gauge does work, meaning it does move while I'm driving (not sure what is correct, I need to research how it should behave when operating normally)
-Parking brake light - Car is on, in park and I set the brake (which sets VERY easily, not sure if that's a concern) but the BRAKE light does not come on
-Fuel gauge as you said floats quite a bit. How can I check the Sender and Ground?
-Phone charger to cigarette lighter...brilliant! Never thought to try that!
Stupid question, when you mention check one side side of the fuse then the other, do you mean while the fuses are in the fuse box, or take the fuses out of the box and check them individually? I assume I'm using a volt meter of some sort?
Finally, "center stack" = Center panel with all the gauges? Or the panel with tach and speedometer?
Sorry... Center stack: yes, center panel with the gauges. Not sure that's the official term!
If the door ajar light works, and the fuel and temp gauges work, you've got ignition voltage to the gauge cluster. Ignore checking the fuse, it's good.
I'd guess that the gauge issues are individual ones... Not one big, easy fix, unfortunately.
The coolant gauge sensor is in the driver side cylinder head, a single green wire attached. With the ignition on and the car hot (watch your hands!) unplug it, and see if the gauge pegs low. Ground the wire to a piece of metal under the hood and it should peg high. That temperature gauge is really just a voltmeter; the sending unit varies resistance with temperature and translates it to temperature.
Under the bottom of your fuel tank there are two wires: a tan one, and a black one. With the ignition on, unplug the tan one and see what the gauge does (it should peg). Then, ground it and look again (should be on empty). The fuel gauge is (you guessed it) just a volt meter.
Oil pressure: you got me. It's mechanical. If it's hooked up, it should work. Not much to go wrong.
Tach: Here is a suggestion.
Unplug it from the distributor. You should see the end on the left of the picture. Hook up a power drill to it and spin it (in reverse on speedos, I'm assuming the same for the tach). See if it works. If it does, it's the tach drive on the distributor (doubtful). If it doesn't, it's between the cable and the instrument itself.
Brake light: could just be a bulb.
Good luck with it all! Trial and error, and getting your hands dirty. Two joys of being a classic Corvette owner.
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"Let them that don't want none have memories of not gettin' any."
- Brother Dave Gardner