Peterbilt 587 headlights

Check the fuses, hi beam should have its own fuse, at least separate from low beam. If that is ok I would then check for power at the headlight connector. Could be the switch, wiring or the chassis node. What year is the truck? Check and clean any grounds on the frame rail near the front of the truck.

 

Relays?

How does anyone see the roads with them covers on?

 

This sometimes happens due to the high beam bulb itself being the issue. Or, it might be a burned wire going to the high beam. It could be the MFS (multi-function switch), but I can't be sure. I would first re-inspect the wiring. I remember that way back in the day, we had this issue with Peterbilt 587 headlights where you had to switch the 2 wires around and then, somehow, it would work.