I have a similar set up at my new house where the old doorbell switch was attached to a standard switch electrical single gang box mounted in stucco. So, my solution was to attach the Ring mounting bracket to a standard cable outlet plate which allows the old wiring to go thru, and has the two screws that will pass thru to mount the plate to the box. I did have to chop the 4 mounting screws down to allow the cable plate to sit flush against the stucco wall. Seems to be secure and works fine.
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