Car in question is a 1982 Camaro Berlinetta with a Chevy 350 swapped in.

1. My factory integrated temperature gauge is not hooked up to anything, and has not been since I've owned the car. The previous owner "installed" a really shitty aftermarket temp gauge that also does not work, and is "mounted" (actually just placed in the car) on the passenger side, routed through the door hinge area. This aftermarket gauge is the tube type, not the wire type (don't know terminology here). Because of this I am not sure the factory gauge even works.2. My turn signals are extremely inconsistent. Both directions behave the same way, albeit very strangely. The exterior and interior turn signal lights flash at completely random intervals, though exterior and interior are in sync with each other. One moment they'll flash very quickly, the next moment they'll flash so slowly it's like they aren't flashing at all.

I immediately thought it must be the turn signal flasher repeater unit under the steering column (see picture), but strangely that is not the problem. I replaced the flasher unit with a new one, and while doing so tested what the turn signals would do without a flasher unit installed at all. Apparently they do the same exact thing. Yup; they still flash even without the flasher unit. I installed the brand new flasher unit and sure enough, it did not fix my problem at all.

I have no idea how a turn signal can still flash without the flasher unit installed, so I'm at a complete loss here. Any thoughts? Thank you for your time!

Just to be sure I'm looking at the correct part, here is an image of the part I replaced. It has two pins on the back side in an "L" configuration that plug in to the module.
https://i.imgur.com/kcWtT2T.jpg

 

Easy answer is ;

You did not replace the turn signal flasher , you replaced the "4 way" (emergency) light flasher . You now need to put the original 4 way flasher unit back where it was , and put the new turn signal flasher into it's proper place . If you do a search here you should turn up pictures of where the turn signal flasher is located , and it is not in the little subpanel you found (commonly referred to as the "convienence center" , even though it ain't too darned convienent to get to !) ....

 

That's exactly where the flasher was located that I replaced. Did you see my picture I linked?

Edit: Some people on the forums are saying the turn signal flasher is located somewhere else, and the hazards are what is in the convenience center. No idea where the other flasher unit is. Can't find anything up under the dash.

Edit 2: Looks like you edited your post and it makes more sense now. I still can't find the dang turn signal flasher though.

 

Still need some advice with my temperature gauge issue, as it's probably much more important than my turn signal.

Edit: Sorry for the double post, my phone didn't want to edit the last post.

 

I have the same problem with your temp gauge and the plug in type gauge. I read in one of the threads that might be a faulty temp sending unit. I have not change
it on mine yet.

 

Factory temp gauge is probably good; they don't often go bad.

Find a green wire coming out of the harness that runs along the inside of the left valve cover. It should run frontwards from under the dist about as far as the PCV valve, then turn out over the valve cover and plug into the temp gauge sending unit in the head between the #1 & #3 spark plugs.

As Orange pointed out, you posted a terrific pic of the "convenience center", and the one in there is NOT the TS flasher. That one is the hazard flasher. The TS flasher is up under the dash in a sort of clip, next to the steering column, but NOT in the "convenience center". Easiest to get to if you lower the column... all ya gotta do for that, is loosen the 2 nuts that hold it up under the dash. You should see it in the sort of "tunnel" left where the column came from, up high, to the pass side of the column of memory serves.

 

So can the original temp gauge and plug in gauge be set up for both to work simultaneously( not that I want to do that)? Or Do I need to disconnect the plug in gauge to allow the electric to work?

 

Depends on whether there's places in the engine you can put em.

Can't run 2 gauges off of 1 sending unit, that much is for sure.

I'd recommend getting rid of the aftermarket one and getting the stock one to work right. Not because it's "accurate" or "better" or any of that; quite the contrary; but rather, because it's not invasive, and it BELONGS there. Almost as though the factory designed and created a place for it to live. It's not like having this foreign WART thing graunched onto your dash somewhere somehow. And in the end, what you're interested in, is NOT the "absolute" temperature of something, anyway; what you need to know is if the cooling system is working (gauge reads the same as it always does) or is broke or breaking (gauge reads something substantially different).

 

That's what I thought; I am glad we are on the same page!