Vacuum Hose Melted, Can't Find Other End 90 Taurus

I'm trying to fix the air in my '90 Taurus GL 3.8L. It is always routed to the defrost vents under the windshield even if I select vent or floor etc.

I read about other people with this problem that said it was a vacuum hose that controlled the air routing. I have a severed hose (about 1/8" diameter) coming through at about the center of the firewall near the top, it's right between two larger (about 3/4" diameter) hoses that come through the firewall also. I'm guessing this is the problem, but I don't know where the hose gets routed to. It was actually melted when I got the car so there was just a ball of melted rubber on the end.

Can someone tell me where this hose gets routed to and if this will fix my air routing problem?

Thanks!
BMagnusen