Oh! The box said that we shouldn't put it closer than 1 ft, but I will try putting the seed trays on top of something to get them closer to the light. Only the brussels sprouts have sprouted up so far, so this will be fairly easy for now.
The fixture is actually seated on nails in the wall, but we taped the side since it was a bit wobbly and as extra precaution against four-legged plant foes.
As for closet space, when we moved in we shoved everything we didn't want to deal with (and that's A LOT of junk and boxes) into the two closets in the apartment so now they're all filled to the brim and daunting to go into.
I meant "stupid" grow lamp in a joking fashion, only that it was so frustrating to find since it was hiding.
It was actually the cheapest of the lights of that nature that had plugs, the other ballasts that came empty had to be hard-wired, and the other plug-in ones with lights were more expensive for some reason. I'm also stubbornly going to find some reason to have it since we searched for it for so long.