Troubleshooting fuseable link failure

I'm assuming all you did was ground one of the field terminals on the alternator. That is correct. The later voltage regulator controls the flow by opening and closing the ground. That's why an alternator will have a field terminal that is isolated from the housing. The stock '68 voltage regulator, like you have, controls the positive feed. For those, the field's return can go directly to ground.

Fusible link normally burns because the battery discharged a ton of current, or tried to. A less likely cause is the alternator sent a ton of current toward the starter realy and battery. But your ammeter would have pegged the charge side if that happened.
I think we have a good explanation and diagrams here: Understanding Charging Systems with Ammeter.
Take an ohmmeter and check to see if the wire is grounded. If it is, start disconnecting connectors and testing each segment. Disconnect and check the alternator too. There's a chance the output side (heavy 'Bat') terminal got grounded.
The diagrams on my website should help you, especially the one at the bottom from my '67.