Again - That still sends out a beacon. Searching for already-paired bluetooth devices still sends a bluetooth frame with your bluetooth MAC address, (which has to be consistent, because that's how bluetooth devices identify each other).
> Searching for already-paired bluetooth devices still sends a bluetooth frame with your bluetooth MAC address, (which has to be consistent, because that's how bluetooth devices identify each other).
It doesn't have to be readable by third parties. Given that the devices are already paired, it's perfectly feasible for that frame to be encrypted gibberish that only the other device can understand.
I think that the math of battery life if you had to decrypt anything that looked like a handshake packet to see if it's for you is the opposite of feasible.