Unknown Brown Wire with Ring Terminal on 66 Barracuda

When I replaced my carpet, I found a brown wire coming down between the firewall and the heater on the passenger side of my 66 Barracuda. It's around 16 gauge and has what appears to be a factory ring terminal.

Any idea what it might be for? I looked over the wiring diagrams but don't see what it might be for. All my heater controls seem to work well. All lights work except for backup lights (there is no switch on the floor shifter). And there is no neutral safety switch connected.

I'm stumped as to what a brown wire with a ring terminal would be for.

Any ideas! Thanks!