* The horn is triggered by a faulty sensor. This could be a problem with the horn switch, the horn relay, or the wiring. If the sensor is malfunctioning, it can send a signal to the horn even when the engine is off.
* The horn is being used as an alarm. Some Dodge Neons are equipped with an alarm system that uses the horn as an audible deterrent. If the alarm is activated, the horn will beep when the engine is off.
* The horn is being triggered by a remote starter. If your Dodge Neon is equipped with a remote starter, it may be possible to trigger the horn by accidentally pressing the wrong button on the remote.
If you are not sure why the horn on your Dodge Neon is beeping when the engine is off, it is best to take it to a qualified mechanic for diagnosis and repair.