1988 Mazda 323 Electrical Problem?

I was recently given a 1988 Mazda 323 hatchback 1.6 liter FI SOHC engine.
It's doing strange things I believe tied into the electrical system.

It has 38K original miles.

It was making a belt squealing sound that has stopped since driving home 200 miles.
Not sure what was causing the belt squeal.

The temperature gauge fluctuates between off the charts HOT back down to cold and vice versa.

This corresponds with the car shifting back and forth between overdrive and 3rd.
Within normal ranges or "hot", it will stay in overdrive.

When it goes back down to "cold" on the temperature gauge, it downshifts back into 3rd gear.

Also, the front blinkers don't work and neither radiator nor condenser fans kick on.

I've thoroughly cleaned the battery posts and clamps and cleaned what appears to be one negative ground connected to the transmission dipstick mount.

There appears to be another ground on a brace on the opposite side of the engine which I have not cleaned yet.

Anyone have any idea where to look first?