With Beatriz Vizcaino, Chia-Wei Liu, and Clint Beharry.

This is what happens when you run 120VAC through relays designed for 12VDC. Your project doesn't work. The relays, as far as we can tell, fused together. This is why the 'Vacant' light didn't turn off when Chia-Wei sat down and why the 'Busy' light didn't turn off when he got up.

Once these relays turned on, they were on.