I believe I know the answer but will ask.

In wiring up a shift light, one of the shift light wires (green) is suppose to connect to negative side of the coil. Can the factory tach wire (e.g. the single wire coming from the engine compartment to the factory tach) be used for this connection? Or is it best to run this green shift light wire directly to the coil?

The two other shift light wires are a ground and an ignition source and are not in question.

I would run a seperate wire.
I would be concerned about voltage issues using a single wire.
Even though they are both tach's, one might use a little different voltage than the other.

I have an MSD box so it has a tach output terminal on it, I have two tachs (one underhood for tuning) and two shift lights (one set at 5K for street driving wired thru an MSD RPM switch, one at 6500 for racing) hooked up to it and all work fine since they all have seperate power supply wires.