On a 3-pin fan, the tachometer signal is a pulse from the hall effect sensor on the fan that detects each revolution of the blades. The resulting signal allows the motherboard to know the RPM of the fan, its not a pure voltage.

I may be missing something obvious, but why not just get rid of the jump-wire to the tachometer signal all together and just use it as a two pin fan on your motherboards three pin header? It should work fine like that, just without any speed feedback. Most half-decent BIOSes that care about tach, also allow you to ignore the signal.

Somehow I don't think I knew it could be ignored. The BIOS was just freaking out at me with the beeping and POST messages and I assumed I'd need to find a way around it. Maybe that's a sign that I don't respond well under pressure or something. 😀

Whatever the case, thanks for providing me with some clarity. It's much appreciated.

Some socket A motherboards have this feature where they won't POST or give power to the CPU if they can't detect a CPU fan being connected (through its RPM monitoring pin.) But those are far and few in between. Even with that said, I don't see how jumping the 12V rail back to he Tachometer pin would do anything useful, as the Tacho pin is indeed a pulsed signal, not a plain DC voltage as paradigital explained above.

I don't think a motherboard could be damaged... but it really depends. If I do remember correctly, I think a few motherboards did have their Chassis and System fans ground the Tacho pin, because they simply didn't use the input from it. So in a case like that, you could get melty wires and/or motherboard traces.
As such, it might be best to cut that wire to avoid any damage.