In order for the car alarm sound to work in vehicles with hydraulics which don't technically have a horn according to the game, the hydraulics have to be removed, the alarm started, then the hydraulics re-added. The same has to be done to stop the alarm.
For some reason, if you pause while the alarm is sounding on a vehicle that has hydraulics, and the alarm finishes while you're still paused, you'll come back to the horn sound playing continuously (not even beep, beep, beep, just beeeeeeeeeeeeeeeeep forever).
But there is a solution - simply exit and re-enter the vehicle.
I may be able to fix this by removing and re-adding the hydraulics after the player unpauses, however as this issue is both a) rare and b) not that impactful, I won't be rushing to fix this.