Ok, I've been looking into the ZG alarm system. As I haven't seen one of these for a few years I'm a bit rusty so I've checked the installation instructions and with a reliable source in the Jeep world.
It is an add-on made by May and Schofield especially for the UK market and fitted to all UK ZGs by Chrysler Jeep Imports UK before shipping to the dealer network. The system comprises of the control unit located behind the far right hand corner of the dash, a complex wiring harness, ultrasonic sensors and a siren located under the PCM on the driver side inner wing under the bonnet.
It is operated by a direct connection to the drivers door central locking motor, which allows the factory keyfob to arm/disarm when locking/unlocking the Jeep. There are no wiring diagrams available, and all the wires to the unit are black for security reasons.
Technical information is pretty scarce but the following may be useful. The M+S unit does not use the CCD bus network in the vehicle like in later versions for other Jeeps. This means that the DRBIII scan tool cannot communicate with it for diagnostics. Instead it has to rely on a large jumper harness connected to the body control module which is located just below the alarm controller in the dash. The system is also connected to the indicator harness so it can flash the lights.
It would appear that the system uses a starter cut controlled by the May and Schofield unit. This is simply a pair of wires spliced into the yellow/red wire in the wiring harness behind the glove box. The fuel system is immobilised by the body control module, which has the factory anti-theft function activated when the alarm is fitted. Once this is activated it cannot be de activated.
The siren is a frequent source of trouble as it is easily damaged by water ingress. It will go off on it's own and is impossible to silence even if completely removed as it has it's own internal power. If the siren is damaged or disconnected it can stop the rest of the system operating correctly, so don't just chop the wires expecting it to stop. You can dismantle it and cut a wire to the speaker, then put it back if the rest of the system still works, or get a replacement from a dealer.
The system can be disconnected if you're feeling brave. Start by stripping the drivers side dash out to access the alarm unit and BCM near the driver's right knee area. You will see there are three large 24 way plugs in the BCM and six in the black alarm module. Remove the three jumper plugs from the BCM and the three original BCM plugs with the coloured wiring from the alarm module. Feed these back down to the BCM and plug them in. They are colour coded to their sockets so you can't get it wrong. Find the large wiring harness behind the glove box and locate the yellow/red starter wire. Cut out the wires spliced in from the alarm harness and reinstate the starter wire. The vehicle should now crank without unlocking with the key fob, but will not start and stay running unless you do so as the BCM will still kill the fuel system. At this point, if you began with a running vehicle, you should still have one. If not, reinstate what you've taken apart and call me a clueless wa**er. If all is well, you can either leave the bits in place or carefully remove the rest of it bit by bit, check the Jeep still runs at every stage so you have an idea what buggered it up if things go pear shaped.
If you are starting with a non starting Jeep don't just blame the alarm straight away. It is always worth disconnecting the battery and leaving for a minute before reconnecting to reboot everything because the drivers door module can crash and disrupt the rest of the CCD BUS network causing all kinds of bother. Deliberately set the alarm off and see if the siren sounds like it should. It should sound very loud and clear. If it sounds muffled or very sick, that could be your problem. If you have recently experienced very wet weather, check the area around the large fuse block in the drivers footwell. Water creeps along the wiring harness through the firewall and into the fuse block causing electrical chaos. Also remember the infamous crank sensor. This can fail and knock out loads of other engine related systems at the same time.
Hope this is of use. Haven't tried it myself, have a go but don't blame me if it doesn't work, I'm only passing the info on!