The tach will work fine with Mopar electronic ignition. It does on my 70 Challenger. Those factory tach circuit boards are NOT accurate.

Also the tach needle is press fit on and should read zero with the ignition key off.

Your tach has 2 parts: 1)the meter movement and 2) the circuit board.

Either one could cause your problem.
This is the best option for new circuit boards: http://rt-eng.com/rte/index.php/Main_Page
There are 2 67-74 boards. The more expensive has an on-board calibrator ckt.

Is your needle on zero with the car shut off? If so then I think your board is most likely bad. They have capacitors that often fail. But it could be a dirty/sticking meter movement causing the needle to remain on zero until you rev it to get it un-stuck.