Coleman Fleetwood 12 volt system problem

You seem to have done a good job of pin-pointing the problem. Somewhere between the kill switch and the converter a connection is lost. If the wires are color coded, as in the link below, you should be able to look at the wires on the kill switch and check that that same wire is hot at the converter. If not, it is likely the fuse, or just a connection on the hot side of the fuse - I say this as the other 12v outputs from the converter seem to be working OK. (outside light, water pump, etc.)

Link to Wiring Diagram