I also notice that the ground wire in the 6 way trailer connector has 12V when you hit the brakes or turn signals.
That is the key, right there, that is the key
you have a bad ground. on the motor home end of the flat 4 connnector
The ground lead is the "Odd" pin on a flat four
Trace the ground wire and see if there is a place where you can ground it to the chassis.
Is this a workhorse issue or a coach builder issue? I don't know.
NOTE 2: I think that ground wire should be at least 10ga, not the hair thin stuff they use on those connectors (That's a Barjan issue, not a Workhorse and not a Chassis builder, but whomever made the blasted connector) I would seriously consider a upgrade on the ground wire.