You mentioned old and thermocouple, so does that mean you have a standing pilot?
If so, then the theromostat only sends 24 vac to the gas valve. Measure the voltage to the gas valve. By turning the thermostat on and off many times, its a good guess you have an issue with the thermostat, thermostat wires, or a sticky gas valve. Measure voltage at valve and tell us more about furnace.
If you have a high efficency gas furnace, then you may have many issues. Need more info.