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Here is something much simpler.
ps, after posting it, I thought of a potential problem. What happens when the key is first turned on before the engine is running? Is the tach signal High or Low? If High, then it needs to be slightly more complicated.
A $2 microcontroller could do this and other things with very few external components.
Not by the time you make an automotive glitch tolerant power supply for the microcontroller, add a switching transistor (because the microcontroller can't drive a relay, etc, etc). Microcontrollers are neat, but don't solve every problem...
Here is something much simpler.
ps, after posting it, I thought of a potential problem. What happens when the key is first turned on before the engine is running? Is the tach signal High or Low? If High, then it needs to be slightly more complicated.
You can capacitively couple Mike's circuit, like the old VOX relays that turned on when audio was present. Given the reliable 12v input waveform it should be very easy and it's a good way to do it.
Another option would be a voltage window detector. You can turn transistor 1 on when input volts > 3v and use a second transistor to turn it off when volts > 9v etc, then connect the relay to transistor 1. This will detect the average DC voltage of the squarewave signal.
An even better idea would be to use the battery warning light wire,works well enough for split charge relays,12 volts Dc when the engine's running and 0 volts when it isn't.Not too sure tis woulld work like this thinking about it now,but wil have a play later.A glitch proof regulator is a good idea irregardless of what way you do this. The first 60 volt load dump will blow the brains out of that little 3904. Likewise for a polarity reversal.
Simple way: Tie onto the stator of the alternator (many if not all of them bring this connection out for use as a tach signal on diesel engines) and feed an AC relay, or rectify it and feed a DC relay.
Typically, the warning light has a ~100 ohm resistor across it to guarantee that the alternator receives it's 12 volts so it can start. One side of the light connects to a switched ignition feed. The other side, of course, is the alternator "I" terminal. Normally this is at 12 volts keeping the light out because you have the same voltage on either side of it. When a fault occurs, the "I" terminal goes to ground illuminating the light. There is no guarantee this wire will tell that the engine is alive or dead, it will tell that the ignition key is in the "on" position or not.