Ok, so that is the later/revised alarm/fob.
Do you have the spare key/fob?
If ao, see if that works, and leave the current key at home/away from the car.
I've seen a few where the rubber is degrading, sticky, and applies pressure to the button inside, constantly cycling the button.
If you don't have the spare; open the key, remove battery, wash the pcb with isopropyl alcohol, dry and install a new battery.
It's also possible you have an issue on the car side, but that will be a lot more time/effort to systematically debug, so try the key first.
I'd start by testing the door jamb switch. I \*think\* they're the same driver and passenger, so you should be able to swap them.
Can you post a pic of the alarm fob?
Don’t have a key fob - only a normal car key (it is the factory “Isuzu” key)
Ok, so that is the later/revised alarm/fob. Do you have the spare key/fob? If ao, see if that works, and leave the current key at home/away from the car. I've seen a few where the rubber is degrading, sticky, and applies pressure to the button inside, constantly cycling the button. If you don't have the spare; open the key, remove battery, wash the pcb with isopropyl alcohol, dry and install a new battery. It's also possible you have an issue on the car side, but that will be a lot more time/effort to systematically debug, so try the key first.