Normally, if a cooling unit works on one heat source, it is good and will work on the other heat source, if the proper heat is applied. However, there are a couple of exceptions.
Some of the older Dometic refrigerators, pre-1972, had two perk tubes--one for 120 volt and the other for gas. It is possible for only one perk tube to become clogged. This would cause the cooling unit to work on one heat source and not the other. Only Dometic model numbers that began with the letter M had two perk tubes, but by no means did all the M series models have two perk tubes. The only way to tell for sure is to remove the insulation pack and look at the pipes. If the electric heat element holder and chimney are welded to the same pipe, the cooling unit has only one perk tube.
Another, but rare exception to the rule of a cooling unit being good if it works on one heat source is a situation where the weld that connects the electric heat element holder or gas chimney to the perk tube or boiler is broken or spotty. If the heat source cannot make good contact with the boiler or perk tube, the cooling unit will not work right.