If you view the end of your T12 cartridge as a stereo plug, I believe it goes like so:
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Sheath is earth
ring is negative terminal
tip is positive terminal
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
The thermocouple is read between positive and negative. Power is also applied between these two terminals.
If you buy a clone 951 handle for it, the ones that are like 10 bucks, the colors of the wires are all screwed up. I believe the Red is earth, green is positive, black is negative. But you can trace them all out yourself using the previous information. All you have to do is wire up the new handle connector like the last one, going by what wire contacts what part of the cartridge... not necessarily by the color of the wire. Hint: I imagine most people with experience in this sort of thing would partially disassemble the handpiece so they can get to the socket, then use a continuity tester to figure out which wire contacts which part of the connector (sheath/ring/tip).