Another mystery wire on my '53 J!

[bearman]

On the right side of the engine, near the temperature sending unit (NOT connected to it), there's a wire that's about 6 inches long with an "O" ring connector on the end just hanging.  Its other end appears to be joined in with a group of wires, part of which goes to the coil and part to the starter, and the other end of this group goes across to the left side of the engine, perhaps to the regulator.  Any ideas?

[Fid]

See if this helps; There are 4 wires which connect to the starter solenoid on the '53 J (three if the car does not have overdrive). Three of them connect to the large, outer-most lug on the solenoid. They are (See in the picture) the large negative cable from the battery (pretty obvious), a heavy gauge brown wire which goes to the "BAT" terminal on the voltage regulator and an orange wire (roughly same gauge as the brown one) which goes up to the overdrive relay if the car is so equipped.
The other wire on the top middle terminal of the solenoid goes through the harness, to the starter button (white originally but likely faded and dust covered so it will appear tan).

[bearman]

Thanks for the explanation and photo, but I don't think it's solved.  BTW, the car runs fine without this wire attached to anything, and I don't have overdrive.  Mysterious!