2004 eclipse tach wire

The reason why you are getting 12volts on it when the vehicle is off is because the engine computer outputs a ground signal to fire the fuel injectors.  Fuel injectors are resistive devices (much like relays) so if you apply a constant 12vdc on one side (like they do) and leave the other side ungrounded (like it is when the motor isn't running) then BOTH wires will read 12vdc.  However, the 12vdc on the other side will be current limited by the resistance of the fuel injector, so it isn't a true 12vdc source.

Once you start the car, the engine computer is outputting a short ground signal to each fuel injector one time per revolution.  Your multimeter is averaging the on/off ratio, which is why the voltage drops.

Things have changed quite a bit over the past few years in terms of multimeters.  You should NOT be using an AC meter for tach monitoring, you should be using a frequency meter (reads in Hz).  You can buy a cheap Craftsman meter for $30 that will read frequency (or you can spend some cash and get a Fluke).  While reading frequency you'll get a constant frequency at idle (in relation to the pulses per revolution) that is actually predictable (a fuel injector on a 4 cylinder motor running at 1000rpm would be around 4 Hz - 4 cycles per second).  As you increase the motor RPM the frequency, too, will raise at a predictable level ( the same moter at 4000 RPM would read close to 16 Hz).

I used to use AC voltage monitoring to measure for a tach signal, but once I got a frequency meter I'll never use AC again.

Here is a link to such a meter - http://www.sears.com/shc/s/p_10153_12605_03482139000P?vName=Tools&cName=Electrical+Shop&sName=Multi-Meters%2C+Testers+%26+Accessories

I actually have several of these meters and I love them.   They are great because they are basically disposable.  If I'm doing basic stuff like alarms/remote start I'll use one of these meters and not worry about dropping or breaking it.  If I'm doing something that requires a high speed meter or something special I'll pull out my Fluke meter.

I would think the LED approach would work better then using a meter set on AC.  At least with the LED you can visually see RPM.  The only issue I would have there is current consumption.  I'm sure they are low current LEDs though, so it's all good!

I'm big on "using the right tool for the right job" and just never had confidence with the AC meter because it was unpredictable.  I had wires that read as tach signals but wouldn't program and such.  But, I've never had a frequency meter tell me wrong!