I have a dash cam too. Mine is not the "in the mirror" type, but I understand every time there's an interruption in power the camera wants to turn the screen on. In your case, the mirror. My camera has settings and I'm sure yours does too. I know I can set my camera to not display the screen at all, 30 seconds, and I think it can display up to 2 minutes.
I'm also wondering if your hard wired power supply (5V with keyed ignition) is wired to something where power drops significantly. If I had to solve your problem for myself I think I would go with a 12 volt relay controlled by a keyed source, the power coming directly from the battery, thus eliminating power sharing on a line that may see more significant voltage drops because of power usage.
Even when I've had weak batteries in cars, seeing voltages drop below 10 volts during starting - I wouldn't think that would kick your camera into a restart. Perhaps your car battery is old and in need of replacement. If it's affecting your camera then that's worth a look. At the very least, rule that possibility out. You DO say it's a 2017 Escape, so the battery SHOULD still be good. But you could have gotten this very Escape in 2016. 3 year old batteries CAN become weak. Not saying it IS, just that it's a possibility. I'd at least look into that.
Putting a capacitor on the 12 volt line - - - the capacitor will feed its power back into the cars electrical system during restart. Unless you put a diode in circuit to prevent the back flow of current. But if I were to go the route of a cap I'd put it on the 5 volt line where it couldn't back feed it's stored charge. But that may mean having to cut into the power harness and adding a capacitor into the circuit. That can become a weak "failure" point in the system.
I've been using dash cams since 2014 and so far have not had the need to prove anything. However, in my wife's car, she had an incident with another driver and road rage where she tried to force my wife to stop on railroad tracks. No train was coming, but you could hear my wife panic. The video was sent to the police and they "had a talk" with the other driver.
I'm also wondering if your hard wired power supply (5V with keyed ignition) is wired to something where power drops significantly. If I had to solve your problem for myself I think I would go with a 12 volt relay controlled by a keyed source, the power coming directly from the battery, thus eliminating power sharing on a line that may see more significant voltage drops because of power usage.
Even when I've had weak batteries in cars, seeing voltages drop below 10 volts during starting - I wouldn't think that would kick your camera into a restart. Perhaps your car battery is old and in need of replacement. If it's affecting your camera then that's worth a look. At the very least, rule that possibility out. You DO say it's a 2017 Escape, so the battery SHOULD still be good. But you could have gotten this very Escape in 2016. 3 year old batteries CAN become weak. Not saying it IS, just that it's a possibility. I'd at least look into that.
Putting a capacitor on the 12 volt line - - - the capacitor will feed its power back into the cars electrical system during restart. Unless you put a diode in circuit to prevent the back flow of current. But if I were to go the route of a cap I'd put it on the 5 volt line where it couldn't back feed it's stored charge. But that may mean having to cut into the power harness and adding a capacitor into the circuit. That can become a weak "failure" point in the system.
I've been using dash cams since 2014 and so far have not had the need to prove anything. However, in my wife's car, she had an incident with another driver and road rage where she tried to force my wife to stop on railroad tracks. No train was coming, but you could hear my wife panic. The video was sent to the police and they "had a talk" with the other driver.