If everything temperature related is working properly, ie. the fan cycles properly, the cooling system isn't overheating and the engine isn't running on a bad mixture, then I would think the problem is in the temperature module, the instrument cluster, or possibly a wire with worn insulation shorting to a bare spot on the frame.

First thing I would do is pull the temperature module and see if the light goes out.  If the light stays on, the problem may be in the instrument cluster.  If it goes out I would suspect the temperature module.  Next thing would be to see if you can get a module to swap with the one on the bike for a positive test.

Yeah, if it's running well and fan cycles as it should with the temp idiot light always on then I'd also suspect something funky with the thermo relay. (The white one on the right side of the relay box.)

Another possible cause for the temp idiot always on is that the VIO/BLK wire from the temp relay (Pin A3) is shorting to ground somewhere between the temp relay and cluster.

When you have the temp relay pulled the idiot light should come on if you ground the socket terminal for the A3 pin - with ignition turned on. (Pin layout is shown on the temp relay.)

All is humming along pleasantly on the low budget rehabilitation of the bike. An interesting thing is holding my attention right now: the temp sensor light is constantly lit, but the coolant seems to be circulating, the fan cycles what I believe to be normally (on and off in about 30 second to 1 minute bursts when in traffic after running the bike for a bit), and plugs/exhaust/running all seem pretty normal. Overflow tank has coolant about halfway up the line.

I’ve read a lot of threads about flickering or worry that the light doesn’t illuminate at all, but it’s been solidly on since the engine ran for the first time in my possession. If the key is on, the light is on.

Figured I’d ask the brain trust here- it seems to me that if the sensor wasn’t functioning at all or was always in low resistance mode, I’d have light on/fan on constantly. The fan seemingly operating as it should is interesting. There’s always the possibility that the temp light has been futzed with and incorporated into the alarm system (non op, thankfully) and it’s representing that now, but I’d hope not.

Can you start the engine?  Start it and try again, I'm pretty sure that if you do, the shifter will work.  Even bumping the starter briefly can help. 

Hi Laitch, I did not make this adjustment. thank you for that info. that being said, and obviously im still trying to figure all this out but if the bike is turned off, wouldnt the clutch not matter when trying to engage other gears like 1 and 2?

I suggest hypothesizing how things might work will not solve this conundrum. Do the basic adjustment as described; double check your work. On a motorcycle that is not running and not rolling, shifting sometimes needs double clutching, sometimes needs the drivetrain jostled but don't do either until you've done the basic adjustment, and you have a full grasp of procedure. You're out in the weeds right now.

Ive . . .completely avoided anything to do with the transmission because I'm novice at building and I'm learning as I go. Only thing mildly related to the transmission that Ive touched has been the new rear sets and adjusting the clutch cable length.

Does this mean that after setting the cable length you did not do a basic clutch adjustment as outlined below? If so, perhaps you should.