View attachment 307209
Will it work? Probably, but I'm not sure how the battery is wired and there's no reason to take a chance. Both the car and the blackvue battery are floating grounds. In general, you should never connect these together. Wiring it properly doesn't cost any more and isn't any more difficult so it's just not worth the chance something goes wrong with tying the grounds.
On the relay idea: A relay is just a switch that can be actuated by a computer instead of manually pressing/fliping. So yeah, if you setup a microcontroller with GPS or something it can automatically turn this on and off depending on location (or whatever other crazy ideas for automation you have). Definitely something to look into if you want an automated solution.