Temperature gauge

Yes/no/yes, possibly.

The first thing I would test or replace would be the sending unit on the water outlet flange.
The Second First thing I would do is to Clean the Battery to frame wire, and frame to engine. If still OEM I would replace it.

Moving on to the sending unit, they do go bad, and I have a HOW DO I FIX them in the Electrical faq's DIY's.
I would suspect on the cluster a flakey gauge, or if your fuel gauge is acting up as well a bad or iffy 10V stabilizer which is a lm7810 device.
You can buy from ebay or dealer for 35-50 dollars even on-line, or use a FA7810-AET for 95 cents from mouser, or an electrical supply house, at that price you can buy a few as in 5, and send me half the price of the remaining 30-40 Dollars I just saved you

Bad grounds on the cluster as well as iffy 12V to it so check your BLACK wire in relation to the Ground wire on the cluster (brown) then compare the differences between pin 14 and Frame. I usually add a frame splice about 5 inches back of the connector on the brown wire with a Scotch-lok wire splicer and the frame with a small pilot hole, sand to bare metal using a ring connector and a self tapping sheet metal screw.

If your connector is like the ones I picture in my how-to's I add one piece of electrical tape under the mylar to force the mylar to make better contact with the pins of the connector.

FA7810-AET didn't work for me at https://www.mouser.com

read up on your DYI's, awesome write ups as usual Briano

before getting the dash instruments all taken apart I did some poking around in the engine compartment, cleaning grounds, and checking electrical functions. I found out a few things: my cooling fan won't run unless I put voltage directly to the motor with a small battery. manually closing the circuit with a wrench at the thermostat valve terminals on the side of the radiator activates the relay, I can hear it clicking, but the fan still doesn't run. my hard wired switch that I installed to manually override the thermostat valve when I lived in Arizona also activates the relay, but the fan still doesn't run. the 30 amp radiator fan fuse is good. so what is left to check to find out why the fan motor isn't getting power?

and to continue on the temp gauge, I looked a bit closer and also noticed the fuel gauge is also acting up. and further more, my hazards were acting funny, sometimes the left hand signals don't blink, and then they do. sometimes the hazard switch on my dash blinks, and sometimes it doesn't. I also intermittently hear one of the relays buzzing randomly, like a warning tone.

Lastly, WTF is the long yellow relay that dangles on its own, and seems to change nothing at all when it is removed?

Don't know about the Yellow one, got a part number?

Back to the fan, IIRC there is supposed to be sort of a direct power to the radiator switch then via the Fan with a relay, so I think that your Radiator switch is Ca-Ca.
Only taking it out and testing it in boiling water will be the go/nogo.

Look at Chris's pages 72-75

Fuel and Temp gauge is either the 10V stabilizer, or the black 12V in or the brown gnd wire to the system.

I would measure the brown to black wire for the same as Battery to frame.

I usually tie a additional ground to the frame behind the cluster by drilling a pilot hole behind the dash, sanding down to metal then use a ring connector and sheet metal screw and attach that via a scotch-loc wire splicers.

Sounds like you have a ground issue on the turns as well the only things in common between the flashers and the turns are the Hazard switch and the turn switch. The real common point is the Flasher relay.

The relays buzzing could be because of a bad ground or water migration to the Fuse Panel.

Try cleaning the grounds and power wires Including the offshoot wires (ones attached to the through-bolt) for both the power and ground side.

turns out the yellow fuse is an oil pressure warning relay.

For the Fan: removed the relay, completed the circuit manually with a wire, the fan ran. opened the relay, water damage. cleaned it up, sealed all the seams shut with epoxy, works fine now.

For the hazards: water damage in the relay. took apart and cleaned it, sealed it, works fine.

Here is where things get interesting: while checking all the remaining relays for water damage, I randomly tried completing their respective circuits manually with a wire, and discovered that when I complete the "bulb check" relay's circuit manually, it resets my temp gauge and fuel gauge, and the gauges appear to work properly even after I disconnect the wire. despite being immaculate on the inside, I also sealed the bulb check relay, and reinstalled it. after about a half hour, I noticed the gauges looked wonky again. so I unplugged the Bulb check relay and completed its circuit manually once more, and the gauges reset themselves perfectly once again at zero. this time I left the relay out, with the circuit disconnected. between 5 and 30 minutes later, (since I didn't sit there watching), the gauges found their way back to their wonky readings, without tampering with any other electrical components, driving or anything else.

What is the bulb check? and what is its relationship to my temp+fuel gauges?