Just finished finding the source of a similar problem with my suburban furnace.
The furnace would start - blower engage - for a few seconds, then stop. A few seconds later, it would start again and more often than not keep running. Eliminated the thermostat as the problem by simply connecting the two thermostat wires together (as Old Biscuit noted). Suspected a sail switch, so pulled the furnace and removed the cover.
On the work bench, the furnace worked fine for several cycles, then quit working all together. Sail switch checked out. but the wire to the blower motor did not show voltage from the relay. First thought was a short n the blower motor, but when I pulled the positive and negative to the motor and applied power, the blower worked. Turned out the ground connection was loose. Proved the old adage that 90% of intermittent problems with DC is a poor ground. The ground for the motor is a blade connection on a ground bus bar at the bottom of the furnace. Vibration and time must have loosened the connection. IF it isn't your thermostat, take a look at the ground connections.
Jim & Lin