I also work remote and have a SAD lamp mounted just an couple of inches above my employer-issued work laptop. (I custom designed and 3d printed a mount for it, in fact.) Basically exactly above and as close to my screen as possible.
It's quite bright (obviously) and does make seeing the screen a little harder, but I crank the monitor brightness up all the way. I don't know specifically that it's given me headaches, but I am prone to headaches. I'll have to pay more attention and see if there is any correlation between headaches and SAD lamp usage for me.
I leave it on at the brightest and whitest setting from 9:00am to 5:00pm (with a break for lunch.)
I will say it's not quite enough. This time of year, even with the SAD lamp, my (self-diagnosed, mild-ish) SAD benefits from sitting out in the sun for 10 minutes or so in the morning before work. But a SAD lamp and no sun is a lot better than no SAD lamp and no sun. I think even when it's overcast (which it is pretty much all the time where I am as well of late) I get benefit from sitting out and getting a little ambient, cloud-filtered light.
This is the specific model of SAD lamp I use. (I've got two of that same model, in fact. One of the AC adapters crapped out not long ago and I ordered a replacement AC adapter from Verilux for way more than what I'd consider reasonable. Works fine again now.) The one I have mounted over my work laptop is mounted in "landscape mode." (Sideways.) I figured that would be better than upright.
Hopefully this is all at least a little bit helpful. I have no idea if you have access to any 3d printers, but if you're interested in my SAD lamp mount models, I'm happy to share.