When you look at that wire connector and you have the 3 wires- Fat red wire bolted to the back which as you correctly guess goes to the battery, then you have the plastic connector that plugs into the alternator with the red and white wires. And on yours the white wire isn't connected to anything. And apologies for asking a dumb question but you are certain the white wire on the pigtail looks like it hasn't been used and not simply broken off from another lead that might be hanging a foot or two away from the alternator at this point?
Anyway, usually both those wires on the pigtail are energized with ignition on. However some are configured as a single wire and don't use that white wire at all.
First thing to do is confirm that both wires show battery voltage with key on. (those wires probably also show voltage with key off but in case a previous owner has installed a relay somewhere check with key on). Often with an alternator replacement or upgrade that red wire on the pigtail might just have a ring terminal put on it and bolted to the output terminal with the charging wire.
Anyway, if you have 12V to both start the engine and for grins make sure you don't show a charge at the BAT terminal on the back of the alternator. NOW, here's where you can start making decisions as Captain- that little white wire? If this alternator has been converted to a "single wire" there's a couple ways that was done and without taking things apart there's not a good way to be certain which way, at least as far as I know. A common way used to be to put a tiny resistor between those 2 terminals, which go to the regulator BTW. If it were me and my boat, I'd strip a clean end on the white wire and while engine is running just give the bare end of the pigtail wire a tap against the battery terminal post and see if the alternator comes to life again and starts charging. If it doesn't, one last diagnostic test for the alternator is if you have clearance and it's safe, look on the back of the alternator and you'll see one hole that looks D shaped. If you look in that hole with a flashlight you should see a metal tab about 3/8" or so in. If you short that tab to ground by using a small screwdriver or pick against the side of the hole it should bypass the regulator and start charging if the problem is the regulator is bad. This is just for diagnostic reasons and actually unnecessary as the kits to rebuild these have the parts for pretty much everything that can go bad so identifying exactly which component has failed is kinda unnecessary.
Anyway I hope that ramble helps a little bit, main thing is to just make certain the white wire hasn't broken off from somewhere else and check the other wire is getting battery voltage and if still no-go try energizing the white wire anyway. If it is still dead then you're going to need to remove and either repair or replace the alternator. If that's the case and there is still an automotive electrical repair business nearby it should only be ~$100 to have yours rebuilt but we can burn that bridge when we get there.
but I will find out tomorrow and post reply
