Electric gate, bell and opener, and only one cable

I need to get a question off my chest again regarding my challenge:

The topic of connecting the Ring doorbell (or rather the power supply) to the gate control is well solved, with the designated terminals/connections.

Does anyone know a way to integrate an electric opening of the gate there? Specifically, I would like to operate a wireless button from inside that then triggers the electric gate opener.

I found something like this on Amaz*on: Funk-Wandsender YWT-8500 von Intertechno

Unplug, and also connect to the control unit, operate the wireless wall transmitter from inside. Would that work like this?

What is still on my mind, the Ring doorbell has the two contacts for the power supply on the back, now that the doorbell is mounted on the post, it surely does not sit airtight and watertight on the post, so rainwater could run behind the housing... Does anyone have an idea about that?

Thanks! :)

Does anyone know a way to integrate an electric opening of the gate there? Specifically, I would like to press a wireless button from inside, which then triggers the electric gate opener.

The gate is delivered with wireless buttons. I don't understand the question. However, you can also install a normal button and use it to open the gate. For this, you need two free wires from the house to the gate control. Then you connect them to terminals 60 and 61.

It is about the gatehouse, not the gate itself. Of course, there is a remote control for that.

Oh, I missed/forgot that. What kind of door opener is it and how do you want to integrate it? Basically, that should be possible with a little tinkering.