Burnt turn signal switch 68 Valiant

Surprise! I'm having trouble with my turn signals. Searching didn't turn up any threads on something like this, though.
One day my turn signals just stopped working. Nothing, nadda. Busted out my test leads and found that it was the switch that had gone kaput.
I went to Napa and bought a new turn signal cam and installed it.
Voila! They work again... however it didn't really "fit". It wouldn't click into place, and if I didn't have the arm centered, the rear would still blink even without the indicator lamp on. Whatever, after a month without signals, I'm just happy to see light.

I drove about 20 miles, and a guy on a motorcycle pulls up next to me and tells me that I have a tail light out. As I pull into the auto parts store to buy another bulb, I turn on the right indicator and it doesn't really flash, but flickers really erratically and then a bit of smoke comes out of the column. After that, nothing. No turn signals, and I have a single working brake light.

I got home and tore it all apart again. The new cam I just bought is melted on the "red" wire side. The little wire is melted into the plastic, and the wire is white like it got very hot. Upon inspection of the original cam, it looks to have had a similar problem, but didn't get as hot so I didn't notice the melted bit until I looked for it.

I jumped the white wire to the tail lamps at the connector so I have working brake lights again. I checked the wires going from the connector under the dash all the way to the trunk, and didn't see any signs of an obvious short. All my light sockets are new/good shape, and the flashers work normally.
I've since ordered an entirely new switch and harness assembly, but I'm a little leery about installing an $80 switch if it's just going to fry itself again.
Any clues on what to check before installing the new switch?