Bluetooth sync button modules ?

I can’t seem to find what I am looking for, Everything I come up with is about putting 2 modules in slave/master mode.

So my question is… Are there any surface mount bluetooth modules that have the capability of using a sync button ?

for instance, now that I have my Nintendo controllers working with the HC-05 modules, I would like to have a button on the receiver and the controller that put it in search and listen mode. Like if you were to sync any bluetooth controller to a system. Maybe Im not searching the with the right words but I feel like Im punching sand in my searches.

Any guidance would be amazing. Thanks in advance.

Would the PCM Sync do this if a unit was hardware set to master and the slave left as is out of box ? like with an RN42 or HC-05 ?