Coolant Light. Randomly come on and off and blinks constantly

Coolant light randomly turns off/on

Coolant level is full. New coolant is in it and old still doing it. Also burped the system.

Water pump okay. Fuse, good.
Not buring oil or mixing.
No, holes in the line. No leaks.
Radiator flushed.
Haven't found a single leak.

I have also noticed the sensor was unplugged from the radiator. Temp gage I think?
When Its unplugged. Coolant light turns off. If plugged in. Coolant light wont shut off.

Im hoping its not inside the headgasket. Im trying to learn to do all my repairs myself. Any thing I'll appreciate it deeply. Also got a few more small issues. Trying to trouble shoot.

AC. WAS COlD, almost 2 whole weeks. When I bought this car. Finding all these random issues. That look to be hidden.
I did a recharge nothing. It did last 2 weeks.
Driver side kinda cold.
Passenger side warm

Heat works pretty good. Ac no. Maybe a bender door?


and RPM running little over 2. When idling goes up and down from 0-2 kinda fast.

I cant find a book or good diagram online. I want to learn all the fixs and how to do it. Rebirth98gh@gmail. Com. I would appreciate it any type of learning.