Temp Guage issues

so my question is should there be a 12V wire going into teh back of the guage
From what I've seen, the 12V terminal is where 12V feeds the limiter inside the temp gauge. The 5V feeds the other gauges, and of course S is for the sender.

Could you connect a jumper from 12V+ to the 12V terminal, ground the case and then see if you get the 5V output at the 5V terminal?

I don't know what resistance values the sender units work with, but if you could get a potentiometer(variable resistor) of say 100 ohms and around 10 or so Watts and put it between the S terminal and ground, you may be able to see the needle move by varying the resistance. That is provided the limiter is working.

All the book shows is some tool with H, M, or L; but it's not much more than a resistance selector box