Problem controlling propane free-standing stove with a millivolt thermostat
Shorting the two wires -- usually -- turns stove on but not always. When thermostat won't start stove, shorting wires will not start stove.

That might indicate a thermocouple problem.  The thermocouple makes the electricity which the millivolt thermostat is turning on and off.  That electricity opens the gas valve.

Stove turns on/off just fine using manual switch in back of stove.

Oh, well, then. If that manual switch is directly operating the gas, that still points to thermocouple.
If it electrically shorts the wires (as the thermostat does), then that would seem to exclude the thermocouple.  That would point to the wiring in the walls, and 99% of the time, a &quot;wiring in the walls&quot; problem is actually a &quot;loose/corroded/faulty terminal connection&quot;.