Chris;

Injectors are not supposed to fire either when Trigger Contacts are static ...but I just looked at Wiring Diag here ( http://www.sw-em.com/1800E%20Wiring%20Diagram.jpg ) again, and both ASS and I had it wrong! (So Sorry!) Controller supplies power to Injectors and one side of all Injectors is tied to Chassis! Please Clean and check this connection for tightness!

I suspect with our incorrect guidance, you might have been interpreting measurements wrong, so please try again!...some notes:

1. Whenever Ignition power is ON, you may only measure Volts (never Ohms)... Ohms can only be measured when component/circuit under test is completely depowered, or an inaccurate/misleading reading will result.
2. Seeing 12V (steadystate), and right across Injector is an immediate indicator of a problem...if that was truly the case (I don't believe it is), Injector would be passing WAAAYYY too much current and burn open!...I suspect something is not as you believe it is, or you are not measuring where you think you are measuring...recheck your method!
3. When Injectors are triggered, they will make an audible click you might be able to hear or pick up with a stethescope, and voltage measured across them at that time should go from 0 to 3V (but since this condition is transient and fast, your meter will probably pick it up, but not indicate it accurately).

Good Hunting! (Sorry again for bad info...it doesn't help with troubleshooting!)