The simple way to avoid that possible constant drain when everything is off is to instead, power the system from one of those power feeds that is only switched on when the engine is running. It will take a bit of investigation, but certainly it will be effective, and much less complicated than any electronic scheme.

 

I can only speak for General-Motors products on the following,
but other makes may have a similar arrangement.

GM Cars/Trucks ( in the late ~90's early ~2000's at least, and maybe newer ),
have what is called a "RAP"-Relay, ( Retained-Accessory-Power ).
This Relay remains hot for approximately ~10-minutes after the Ignition-Switch is turned Off.
This would be a great source of Power for this, and many other similar types of projects.

This type of knowledge is what makes having a Factory-Service-Manual worthwhile.
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.
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View attachment 337661
The motor has its own fuse and is wired directly to constant power. • • • • •
[edit] I hope this doesn't drain your battery. That's a definite concern, since I don't know how the motor is wired internally. [end edit]

The simple way to avoid that possible constant drain when everything is off is to instead, power the system from one of those power feeds that is only switched on when the engine is running.

See post #7