Oh. That's dumb. I guess I've been playing it wrong all this time.
Wait, what is even the point of the antimagic eye, then? I thought the whole point of the beholder is that it disables your magical stuff and then shoots lasers at you. That's what's scary about it. If the antimagic eye disables its own eye rays, then when is it ever going to use the antimagic eye? Unless the DM is all like "the wizard's on the left, so it'll just look at the wizard with the antimagic eye and shoot lasers at the fighter", but that requires way more tactical minutiae than I want to put up with (and depends on how much control it can be assumed to have over the precise edge of its peripheral antimagic vision...). I think I'm going to keep playing it my way, but that's a houserule.
Anyway, as for the present dilemma (beholder vs. darkness RAW)...
As a DM, how would I adjudicate this situation? Well, what would you expect if it was a movie or whatever? Something casts darkness around itself... and the beholders just shoot a ton of lasers into the darkness until the thing dies.
The description explicitly says that the beholder "shoots rays." I will not accept that it can't shoot them wildly into darkness. That's what lasers are for, as far as I'm concerned. So, forget the "it can see" clause. I see this as less of a houserule, and more like errata, since the rule is obviously broken and needs a fix. I guess I'd have the characters in the darkness make two saving throws: One to see if they're even actually hit by the ray, and if they fail, they make a second save to resolve the ray's effect (so, if they succeed on this second save, they still take half damage or whatever).
The other option that occurs to me is that the beholder can open its antimagic eye, point whatever eyestalks at the now-visible target, then close the antimagic eye a split-second before firing.