Arduino and tachometer from 12V car battery gen

I'm not much on car mechanics, but are you talking about the output from an "alternator" or an old fashioned "generator"?
If I ain't mistaken, I believe the output of an alternator comes out in three-phase AC, which is actually three simultaneous AC voltages coming out at once, on three or more conductors. If you read between two of them you should get one AC voltage reading at whatever freq. that might be, and all three freqs. should be the same.

Like I said, I'm not a car mechanic, but three-phase is three-phase, which I haven't worked with or studied for quite a few years, and I'm not even sure if that's how car alternators operate. There are probably circuit diagrams for frequency analysers/counters to be found on the internet; maybe one or more of them could be applied to an Arduino.

I'm sorry I can't be of much more help, but thought I would add some information.
Patrick