Why not simply get an ALTERNATE ACTION push button switch?? Nothing else required: Push and it is ON, push again and it is OFF.

I'm trying to make use of an existing switch to keep an "OEM" look with new functionality.

 

I'm trying to make use of an existing switch to keep an "OEM" look with new functionality.

This Latching relay Module with a few extra components does work with a +12 volt momentary input.
Verfied operation on bench test.