If I hit the brakes on my Cutlass, the temperature gauge jumps 5 degrees and the volt gauge drops almost 1 volt. As soon as I take my foot off the brake, everything goes back to normal. What in the world would cause this?

Presuming your temperature gauge is electric, a voltage drop will potentially cause a change. Electric gauges depend on regulated voltage for their signal. Voltage change reflects a gauge change...

Sounds like you've got some grounding issues....brake lights might be looking for ground through other components because they aren't grounded properly. Seen this many times, especially on older cars with some rust/corrosion buildup in light sockets, etc....

Are these gauges analog or digital ? Are you getting these readings by eye or are they recorded ? Are you running an alternator ? Where is the battery located ? Is the battery a wet cell or AGM type battery ? Are the brake lights actually being used ?

What Coloradoracer said. You have a broken, corroded or lose ground (all all the above). That would be where I start looking. And since it only happens when you hit the brakes, disconnect the brake light switch completely. If it stops acting up, the faulty ground is probably in the brake light wiring harness or the switch itself.

Just gonna put this out there i have seen cut of switches do very weird things. Not saying that i
s your problem but they are pretty inexpensive.