The rule requires ONE working anti collision light system. In any other scenario I can think of, if the FAA requires one of something and there aren’t other factors (KOEL, MEL, etc) complicating the issue, failure of redundant equipment is not a grounding item. For example, you have two transponders and one fails and is legally deferred and placarded. Are you going to still notify ATC one hour prior to entering 91.215 airspace? No, of course you’re not. Same thing with anti collision lights. You still have one working set? Good, roll with it.
One thing to be wary of is that a wingtip strobe system does not necessarily meet all requirements of an anti collision light system. The only way I know of for a pilot to check would be to consult the KOEL if the aircraft has one (which, since you didn’t mention it anywhere in the discussion, I’m going to assume your aircraft doesn’t) It would usually tell you that EITHER the strobes OR the beacon must be operable for night flight.
Edit: I think I see where the miscommunication is coming from. I’m operating under the premise of the tail beacon and the wingtip strobes each separately meeting the requirements of an anti collision light system but you’re on the belief that the three lights together constitute a single system. I’m not actually sure who is right there.
