Yep, sounds like somethings up with the airplane, wiring, electrical noise, localized rf or emf, poor grounding, etc. E.I. stuff is pretty good from what I've seen. Installed their R-1 tach in several airplanes and never had one fail. Two of them have been in service 15+ years with no issues.
Check it out one step at a time and see if you can identify where the problem is.
Try pulling the tach and power it up on the workbench, see if it reads zero. If it does then connect it to your airplane's power without mounting it to the airframe. If it still reads zero then connect one of the leads from the mag switch, if that's fine then connect the other lead. Still reading zero? Then try mounting it in the panel.
Hopefully one of these steps will reveal where the 2000 rpm indication is coming from.
