You work like the original A-150, your paper spawns in the most recent room, you check all grey lockers and fridges in said room, go back to your paper and despawn
Also unlike other entities, instead of just making goofy sounds the Billy's would just repeat their own sentence over and over again
For example Purple Billy says "Hi I am purple Billy and I check blue lockers" and Billy says "Hi I am Billy from the hit game Interminable Rooms yayayayayayayayyyayaya"