2nd Gen Dodge Ram owners: Smell something burning?

Here's a short video showing the melted plug from my 1998.5 Dodge dually. I was smelling burnt electronics driving home in the rain... I thought it was something way worse until I remembered this is a big issue with our trucks. I think this affects Dakotas as well. I am running stock headlights and cab markers with no fogs by the way. I wasn't pulling a trailer either.
Adding relays to drop wattage through the plunger-style switch helps but I don't think it completely solves the overheating issue. Swapping out to LEDs could help (not ready to do that just yet either).
I have another video showing what I used to replace this switch, and similarities between two different plunger switches.
*LMC sells a $25 relay harness for 1994-2002 that I'm going to have to install... Probably at the same price as a DIY version, but (from what I've read) it's too short, doesn't include the relays or fuse holders. Daniel Stern Lighting (dot com) has one for $229.