Lately, on startup of a Goodman GMP100-3, it will immediately shut off. Turning main power on and off with a few seconds delay will get unit going by this forcing. Raising and lowering thermostat will eventually get it going. Leaving the unit alone will result in the furnace eventually continuing on its own normally. Fortunately! Then it acts up again.
I'm thinking the Sears digital thermostat is okay as the metered output conditions of the wiring is the same when the furnace is running or acting up. Would one of the many sensors cause this? Thanks for any help you can give me. (The Thermostat is about 25 years old. The furnace was installed 1/96).

Try cleaning the flame sensor.