Joe -
Are you sure you need to do this at all? As I recall, Rocky Mtn Ray (our Tundra guru) didn't have a problem running his refrig on DC while towing. See his comments in the thread at
http://www.trailmanorowners.com/foru...ead.php?t=4909
As for attaching the new wire to the Bargman connector. I'm not sure it is as easy as it sounds. Many (most?) OEM Bargman connectors are molded, not screwed together. This is good, because it makes them rugged and waterproof. But there is no way to open a molded connector - the best you can do is splice the new wire into the old one, before it gets to the connector. And when you splice it, you open it up to moisture penetration, corrosion, and failure.
I installed a new #10 circuit in my Explorer, just as you are contemplating. I really didn't want to break into the Bargman and risk moisture-related failure, so I installed a separate connector beside the Bargman, and ran the new wire all the way through to the TM battery. Overkill? Almost certainly. But the cost of the overkill was small, whereas the cost of doing it wrong would have been large. It made sense to me to overkill. See the result, further down in the same thread referenced above.
Bottom line, I really needed the new charging wire, so I was willing to pay the cost. But if your Tundra doesn't really need it, that's a different story.
Bill