The red wire, as it comes through the firewall, is there to feed the dashboard, interior lights etc.
IMHO, you don't need to bypass the ammeter. By wiring the starter relay directly to the alternator, you have bypassed most of the current draw across the ammeter. In other words, the only current across the ammeter is the draw from the interior of the car. The needle won't move as much, but it can still be a good indication of how things are working (or not working).
I also would not disconnect the ammeter..... If you want to bypass it, put a jumper wire across the two connections. Some cars have a connection in the circuit board that takes power from the ammeter connection. Not all... some do, some don't.
One other thing, install a volt meter.