So looking at the wiring diagrams for that car, the ABS system gets power from the battery, just like every other electrical device in the car. There isn't any other connections to the alternator except standard fused power.

Here are the connections on the alternator plug. I'm going off of what they SHOULD be, so if they're not connected properly at the alternator plug (or at the other end) then my description of their behavior may be completely different.

The white/blue wire (pin 3?) on the alt plug is the lamp wire, which turns the charging light on. It can't cause a problem like you're talking about, the regulator grounds the wire to turn the light on and ungrounds it to turn the light off. It goes to the fuse box under the dash.

The white/green wire (pin 2?) is the normal/low charge control from the ECU. The ECU grounds this wire during low load to save gas (less engine load from the alternator). This is probably the wire you're talking about grounding to test the alternator. It goes right to the ECU.

The white/red wire (pin 4?) is the field circuit monitor, and is used by the ECU to monitor when the regulator turns on the field circuit (internally) to make the alternator charge. It goes right to the ECU.

The black/yellow wire (pin 1?) is from the ignition, and supplies power to the regulator assembly. Power has to be there for the alternator to charge.

There is also the ELD wire that goes from the underhood fuse box to the ECU. The big (main power) white wire on the alternator output stud is monitored by the ECU and is part of how the ECU decides to switch charging modes (to low or normal), etc.

Ok, exactly what wire color are you talking about? It's your turn, you need to verify what is where and that everything is connected properly at both ends.

Is this an engine swap by the way?