By switch, is this to mean the main headlamp switch ?
The hi-low beam is controlled by the MFS, which could cause issue with the headlamps ( and other things ).
When you turn on the main headlamp switch, and have no headlamps and :
1. Use the FTP ( Flash to pass or pull back on the MFS ) what happens ?
2. push the MFS forward ( enable high beams ) what happens ?
With the Main headlamp switch in the on ( headlamps on position ) and the MFS in the low position ( pull back to FTP position, and release to confirm ). Remove Fuses #26 & #28 from the junction box ( cab ) and use a meter to check both sides of the socket. Neg to a known good ground, and probe both sides of the fuse position #26 & #28, what do you get ? I am assuming that this is +12 V at the connector side, as you post did make note of this.
1997 EVTM 85-1 ( headlamps )
MFS test procedure :
If you want to retry the tests above with the steering wheel column in a different position, that might make a difference also ( getting the connector to slide together some times ). Usually a problem MFS is with the connector under the steering wheel column cover, when it pulls apart, and the contacts discolor and loose contact ( general statement about some MFS problems, not specifically your problem ).