I almost missed this one.
I wonder if the light bulb is aftermarket like a led light. I've seen them do some really weird things. I would bet that the horn and the interior light are on the same circuit (fuse). The horn is essentially an oscillator creating a buzz that flexes a diaphragm (speaker). Somehow that off and on bit from the horn is causing electrical noise. Most electrical components that oscillate will have a diode shunt to dissipate inductive current. How do I know this? Because I am an electrical engineer. Things like relays and solenoids will have the diode to prevent spikes in the electrical system. The horn is essentially a solenoid that operates at a high frequency.
If you are interested, how this works is any inductor (anything with a coil of wire) will build a magnetic field. When the current is turned off, the magnetic field collapses. When this happens the collapse of the magnetic field will induce current back into the coil. To prevent the current from going places not intended, diodes (one way electrical valves) are put in place to shunt the current. These will be built into most devices.
I would bet that the horn itself is the source of the problem. If it is an old car, I wouldn't worry about it. If it is a new car, it could play havoc on the computer.
Old car idk about the horn circuit but it comes on with the cigarette lighter... So you're saying a diode died possibly?
Update: it was a fuse and the power was sneaking through