I am adding access control to the garage door of a residence that already has a Liftmaster (Chamberlain) unit in place.  The idea is that a valid access will briefly energize a relay, which would be akin to pressing the wall button.

Foolishly, I thought that momentarily breaking the circuit (i.e, cause an open) between the existing switch and controller would do this, but that didn't work.  I have since learned that the doorbell-style switch is not merely breaking the circuit, and the control panel is looking for a condition beyond merely a momentary open circuit.

Any ideas?  My ultimate constraints are that the existing lighted-doorbell-switch still has to work, and that my method of control is a dry contact relay.

I see that someone had a similar challenge few months back.

Thanks in advance.