What does this run to?

I'm in the process of getting my 66 freshened up so to say. I'm currently installing the new wiring harness and while in the bay I noticed a hose that's unhooked. It runs through the firewall and into the cab into a funny spot. I've got pics below.

Is this the Performance Gauge connector? I had thought that would be a hose through and through. The gentleman that had the car prior to me had a lot of things unhooked and the only thing in the car that half way worked other than it starting was the headlights. I don't have a manual for the car so I figured I would pick your more experienced brains.