Not sure why you would want to do this unless you are setting up a business to test tachos
Hmmm … the problem is , if it works with your relay , will it work on the car ? Maybe, maybe not …if it didn’t work is the tachometer faulty or your circuit ?
I think you need to be switching a real coil which needs a transistor that can stand the high voltage generated . If I was doing it I’d google “ electronic ignition”. - recall making transistorised ignition back in the 1970’s , but sure what I used back then
Have you tried the 'relay coil as inductor' and transistor switch method? Just hook it to an Arduino pin and use the 'tone(pin, frequency);' function to send it a test signal. I'm thinking any 12V relay coil will do.