There are small resistor-capacitor networks connected to the inputs, before the go into the actual input IC's. Frequently on these Atari games, the caps will either go bad, or get cracked/broken (as they are often the glass-encased type). I just repaired a Tempest myself with the exact issue (except it was on one of the coin switches).
The first thing, if you have ruled out the wiring, to do would be find which cap corresponds to that input (in the schematics). You can try measuring with a DMM across it, and comparing to the other caps near it, for the other inputs, and seeing if it is any lower, as they will become on the order of a few hundred ohms when they go bad.
If it is low, you can remove the cap, which will temporarily fix the issue. But you should replace it longer term. It's a 0.1uF 50V axial cap. The replacement does not need to be the same glass type. I get them from Great Plains Electronics, but anyplace will have them.
If it's not the cap, it may be the input IC that it's connected to (which may have a stuck output), but the cap is more likely.