You might have the old style millivolt generator pilot. The pilot actually generates the small amount of electric power the system needs to operate and there for it will not have a regular electric line from your electric panel attached. If you turn the pilot off that will stop the flow of electric.
NOTE:If you are going to replace the thermostat you will need to get one that will work with a millivolt system. It should be marked on the box on on the instructions if it is compatable. Many thermostats for sale now days will not work with your system.
Another note: The furnace you have is a real gas hog. Have you ever considered replacing it with a newer high efficiency unit? The reason I ask is because a new high efficiency furnace will more than cut your gas bill in half and that is big buck savings for most people.