Sounds like the lights have a bad ground, but that light is finding a path to ground through the horn relay.
I would first check the instrument panel ground wire and make sure its tight. It will be connected to a grounding post on the emergency brake mechanism (earlier trucks), or connected to grounding block mounted up under the dash (later trucks).
The plastic twist-in housing around each instrument panel light is also a little finicky about where it makes the best contact. For a problem with individual lights you usually have to clean up the contacts and play with it a little (twist it back and forth) to make sure it is making good contact with the wiring overlay. If you still have the original lights they can be inserted either way, but if you have LED lights they are polarized and will only work one way in the socket.
Bruce