Are you talking about the Red lead in the gray 6 pin connector ?
EVTM shows it to be hot at all times.
Page 15 of the trailer tow install directions does not make a note either way :
If you look at the diagram, F105 is fed from 2 other fuses ( have not located those 2 yet ).
If I got the correct wire, it should be a 10 or 12 AWG wire, hot at all times. Keep in mind John might have actually tracked down with a meter that it is only hot in the run position, or run / assy, which would be a case of the EVTM being wrong, and one of those other 2 fuses only being hot in the run position.