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
In response to the last 2 posts, I have also heard of "small" V8s having issues pulling these large popups. I would say it's mainly due to the amount of stuff that you can pack in them - considerably more storage space than the low wall versions.
I'm still wondering how there was no mention by the author of being at the tow limits in a Trailer Life issue about a Honda Ridgeline v6 pulling a Lance hardside trailer. That was at 6000-7000' elevation too.