I'm NOT looking for a KVM switch, so please don't even mention them.

Synergy doesn't do what I want because it only types on the machine that has the mouse on its desktop.
I want something that Splits the signal from the keyboard, and sends the keystrokes to BOTH systems simultaneously.

Is this at all possible?

I don't think it's possible.

If I recall keyboard interfaces are two way. Your keypresses send data, but hardware acknowledgements will have problems because of multiple paths and sync issues. Hardware collision will likely even prevent such a setup from even booting up.

I don't think its possible either. But if you explain WHY you want to do this, we may be able to suggest alternatives.