The OP very clearly said that when he selects Hi beam, that both headlights go OUT. Obviously, can't be a shutter problem. The F3 doesn't have shutters, anyway. The 2018 F3L North America version - utilizes a duel filament bulb and two relays. One for Hi Beam and one for Low beam. When Hi beams are selected, the Low beam relay drops out de-energizing the Low beam filament, and the Hi beam relay picks up, energizing the Hi beam filament.
Both relays are controlled by the Main Headlamp Relay - R6 - in the Left Side fuse box. (Left side as you are sitting on the bike, BTW. ) That one appears to be working.
For the OP then, the other two relays are in the right side fuse box - R1 for Hi and R2 for Lo. R2 appears to be working because the Low beam filament is turning off. R1 appears like it could be your culprit, because the Hi beam filament is not turning on. Remove it, clean it, re-install it to see if it works then, or replace it. Along with that, double check J-Case fuse J5, in the RFB, again. Don’t just look at it. Remove and check or replace.
PS - and yes, it's not unheard of for a rider to discover both bulbs burned out. All depends on when you last looked at them ON THE HI BEAM SETTING. Unless you have a reason to suspect it, I would sure replace bulbs before I went tearing into the thing looking for wiring issues.