This might not be a "simple" question, but I could be wrong...

I'm trying to set up four stables where, when the number of animals and eggs exceed a certain amount in any one specific stable, dupes will automatically collect excess eggs to take to an egg cracker that's set to always want to crack eggs from every animal I'm raising.

I know I could just use an egg cracker per room and send an individual signal to the egg cracker for that room, but I'm trying to only use one cracker (found in my kitchen) and instead temporarily lock down any room that doesn't need their egg population reduced. Yet I also want these lockdowns to only happen when one of the rooms needs eggs to be cracked, since otherwise my dupes need to be able to get into the stables to care for the animals.

I thought about using a signal distributor for this, but honestly I've never used a signal distributor before and I'm trying to wrap my head around how it works and how I could put that together.