1991 Chevy Corsica Coolant leak from firewall valve

When I fill the radiator, after about half of what I normally put in, coolant begins to pour out of a valve coming out of the firewall. If I stop filling, it stops dripping after a while, and when I put more in, it continues to come out. When the car is running, no matter if heating or air are turned on or off, a steady stream will continue to come out of the valve.

The valve is a black valve, slightly to the passenger-side of center, with a black rubber elbow fitting pointing straight down. (It is located next to a long metal hose that carries coolant through the firewall, under the car, and back out next to it.) I can't find any other place this might be able to connect with to close the gap in the loop. Any ideas?