Disable Wireless Auto when not in car

I recently bought a Wireless Android Auto box for my car which only had Wired Android Auto before. It works perfectly when I'm driving. That part I'm very happy about, coupled with a wireless charger/holder it's easy and convenient.

What's not so good is that whenever my car wakes up to charge the 12V battery (my car is an EV) the Wireless Auto box wakes as well and my phone tries to connect to it. Last night I was talking to my mother on the phone in my living room and suddenly the call was transferred to my car outside.

I'm recently moved from IOS to Android, so I'm unsure what the best way to remedy this is. I've thought about a few possible solutions:

• Use Tasker to shut off Android Auto when I'm at home with geofencing or Wifi network (Don't know if this is possible)
• Unplug the Wireless Auto box when I park at home (Not ideal)
• Make a physical switch that connects/disconnect the Wireless Auto box depending on whether someone is sitting in the front seat (Seems like a loot of work)
• Ask here to get an instant reply with the one setting on my phone I need to toggle to fix this (I do hope this is the one :) )

Have any of you had the same problem, and if so, how did you fix it?

Technical details: Pixel 8 Pro running GrapheneOS. Car is a Hyundai Kona 2020.