[Photoman]

Yes, replace that wire with a larger one and run it through a fuse to the battery pos. At the alternator the original large white wire connects on to the "B" (large) terminal. Where it connects on to the "B" terminal there are actually 2 white wires in the lug connector. A smaller and a larger wire which you are replacing. The smaller white wire should be cut and then crimped in the new lug of the new larger white wire.
To sum up, the larger white wire gets increased in size from the alternator "B" terminal to the battery positive terminal and needs a fuse. The smaller stock white wire that was also connected to the alternator "B" terminal with the larger stock white wire still needs to have power so should be crimped in with the new wire lug.


Bill

Edit > If this is not clear and you need to get going, just run another larger wire through a fuse from the alternator "B" post to the battery positive. In effect increasing the size of the stock large white wire while preserving the small white wire connection at the alternator. This will work but personally I don't like it as a permanent clean solution (double connections, double fuses). The small white wire is a power feed for the under hood and in dash fuse boxes.
The confusion is the small white wire splits several times to feed power to the above mentioned places. All of that is irrelevant. The important thing is along with the larger white wire, it starts off at the alternator "B" post so needs to be included in any new wiring to have power.