Temp gauge bouncing from cold to hot and back to cold over and over again.

Thermal instruments are not chassis grounded (other than the 3 post gauges with limiter inside).
The low voltage goes in on 1 stud (which is which makes no diffetence), through the gauge winding and out on other stud to variable ground signal provided by a senders path to ground (senders don't send squat). If you have a chassis ground at a 2 post guage can, you have a problem.