It's probably the horn switch in the steering wheel itself. In order for the horn to "toot" the circuit needs to be completed between the battery and the horn, and the switch is the most likely culprit. It could be affected by things as subtle as temperature or pressure changes if it is faulty. I had a horn switch "toot" whenever the daytime temptress were hot (>80) and the evening temps were cool (<50).
If your neon has airbags be sure to disconnect the negative battery terminal (good idea anytime fooling with the electrical system) and wait and hour or so (to let the capacitors dissipate their charges) before tearing into your steering wheel.