The regulator bypass jumps the brown wire to the white wire and the red wire to the blue wire.
The white wire goes to the alternator plug and connects to the R terminal on the alternator and the blue wire connects to the F terminal on the alternator which you don't show as having in the adapter with the brown wire.
The alternator must be internally regulated so the terminals would be labeled 1 and 2
where 1 is the brown wire and 2 is the blue wire.
Certain years of the alternator look like internal regulated but are still external. The year you have might be one of those. Pull the plug off and check the connectors inside. If they look like this I I it is externally regulated and needs the external regulator, if they look like this -- -- then it is internally regulated .
OK, going back and looking at the alternator and thinking about what you have said. I think you have a newer CS style alternator that came after the SI series internally regulated alternators. They started in the late eighties and were completely different.
Look for the letters P L I S on the plug into the alternator. Some of them required that the red/blue wire plugged into the S terminal and the brown/white wire plugged into the L terminal. Others only needed to have the brown wire plugged into the L terminal and the voltage sensing was done internally. The corrosion on the white wire might explain why the alternator quit charging or the alternator went Tango Uniform on you.
Here are some pictures to help.
