After getting a new helmet that does not have a sun visor, I went searching for a visor that is thin enough to fit under a helmet. Just got this 2-oz. Visor Buff:
...and can't believe how useful it is. The visor is just the right length and angle for under a helmet. The visor can be flipped up during a downhill section to allow full visibility. The material is thin so that I didn't have to adjust the chin straps on the helmet. It provides some sun protection for my neck (though it's not full coverage).
Here's what else I have made it do:
3. Open-air visor
4. Baseball cap
5. Baseball cap with neck coverage from the sun
6. Towel or handkerchief in camp
So I'm going to leave my towel and neckwarmer behind on the next overnight bikepacking trip, and just bring this.
It might go hiking with me, too, though the sun coverage is not as good as with my regular hat.
I'm in the U.S., the shipping price from Europe was reasonable and it arrived fast.