Anyone know this connection part name?

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Might call it a voltage sense tab, but the whole piece is titled 'wire frame #2. Here is the complete assembly, which is the only way to purchase it : 8216547040 - Wire, frame, no. 2. Battery, electrical - Genuine Toyota Part
- be sure to click on, or call the surrounding dealers for the best price. My lowest purchase price has been $55 with free shipping.

You might try soldering a small piece of rj11 or similar wire to bridge the broken gap macgyver style. But the new part is so cheap, best to replace it at once before others break off as well. Be careful not to over torque the nuts during installation.

Where in CA are you nearest, maybe another member has an old wire frame laying around that can be used for parts.

FYI : you're moderated until you've posted 5 times.

 

Assuming that the wire is still in reasonably good shape, you should be able to get a "spade clip" at any auto parts store and crimp/solder the wire to it.

 

Not sure which part of the bay would cause a "new" harness to corrode in 3.5 years, do you have any water leaks into the interior?

The torque on those nuts is 48 INCH pounds, aka 4 FOOT pounds, basically not very much pressure.

If needed, you can borrow my 1/4 inch torque wrench. Just hit the 'conversation' button or send a PM.

 

They all should be copper alloy inside.
Having it tin coated should not create a problem.

 

Repair Manual excerpt: