Excellent summary of the symptoms. It helps to narrow down the possibilities.
In the case of "flash-to-pass", the power flow is in this order:
Battery
30A fuse located in the box next to the battery
Multifunction switch
Fuse located under the instrument panel
Junction point where 4 loads are wired together . . . .
. . . R hi beam lamp
. . . L hi beam lamp
. . . Instrument cluster hi-beam indicator
. . . fog light cutout relay
Ground
The fog light cutout relay works OK, which suggests power is reaching the junction point (wiring splice), and all the fuses, as well as the dimmer switch, are working.
Two quick tests to do:
-1- Check the instrument panel indicator to see if it goes on, both at flash-to-pass and steady high beam positions of the dimmer switch.
-2- Go out and look at the headlights at night, to see if the hi-beams are actually turning on, but are dim.
If test 1 fails (or the indicator is on-but-dim), and you have dim hi-beams, it could still be the dimmer switch at fault. It may pass enough current to operate the fog light cutout relay, but not enough to fully turn on the lights.
If the panel indicator comes on nice and bright, and the hi-beam lamps are both completely dark (not dim), I would try 1 new bulb and see what happens. While it would be highly unusual for both high beam filaments to fail at once, one could have failed a couple of weeks earlier and you just didn't notice.
If a the new bulb still does not work, we are pretty much left with a wiring problem.