Is there a rule stating that when not in use, arms room weapon racks must be locked, and/or only one rack can be open at a time?

I don't remember if this was just a thing we did or if it was reg. If AR 190-11 doesn't say it then you can check the DA Pam. I'm pretty sure - if I remember it correctly - weapons had to remain behind two locks; if in, say, a connex, they had to remain locked in the cages because the only other lock was the connex door. If behind the arms room heavy door and the gate door they could remain unlocked in the cages. Don't quote me on that though; it has been quite a while since I ran an arms room (2009-2011).

Don't know about only one being open at a time but I do know when you don't need in them they need to be kept locked, It is in the physical security inspection checklist.

We kept our empty racks locked so we would not have to hunt up a lock and key for them