Button card that shows status of one entity and "presses" another

I’m very new to HA although coming from ~10 years of messing around with home automation so still in the “trying to do simple things to learn the basics” stage as I migrate from Homeseer.

This may well be obvious, but I can’t find an answer because I likely don’t even know the right terms to search for, but I’ve setup an integration to my alarm panel, and I have an entity for a sensor on our garage doors (we’ll call it DoorStatus) that reports whether the door is open or closed, as well as an entity for a virtual button from the alarm panel that basically triggers a relay to toggle the garage door open or closed, similar to someone pressing the remote button to “toggle” the garage door opener (call it DoorButton).

I was quite pleased with myself in putting an entity status card in my UI that shows the status of our garage doors using the DoorStatus entity, and changed the icon to a nice garage door. However, I can’t figure out how to tap the image and have HA toggle DoorButton rather than just showing the history for DoorStatus. I also tried a button card, and trolled through the service menu but couldn’t see a way to activate DoorButton by tapping the icon.

Do I need to do something in YAML, or create a custom card? Any hints/guidance would be very appreciated and thanks for your help!