Air handler unit stops running. Starts when motor touched with metal
I had a similar issue and could have sworn it was mechanical/electrical.  I had a service man come in and he removed the air filter from the handler.  It started right up afterwards (i am unsure if there was a reset switch he had to trip).  He mentioned that my air handler will shut off if there is a great enough pressure difference between the supply and handler sides of the filter.  Never thought of that but worth a try before you spend the monies!