First test the battery voltage at the back of the refg.as noted above. Anything over 13.5 will shorten the bulb life
It would be almost impossible to tell if the light was staying on by just opening the door. The light will heat up much faster than you can react.
You can go to the back of the Refg. and remove one of the wires going to the light. With one side open put your volt meter between the terminal and the wire. If you see voltage there the door switch is closed and the light will be open while the door is closed.
If the light is on while the door is closed I would assume you would also see higher temperatures in the refg. 7 watts is a lot of heat to a small refg.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles