When I use my key pod to unlock my Jag. it triggers the alarm. I then have to rush and put the key in the ignition and turn it to disarm it. Any thoughts on repair? Thanks

 

It's not broken. See handbook.

 

When you unlock it using the key the alarm system beeps until you've put the key in the ignition. If the passenger door is opened before you've got the key in the ignotion the alarm will go off.

 

Low battery, has happened to me many times if I lock the car. Would not start after either and set it off again.

 

As I posted, it's not broken. Battery is irrelevant.

 

This is exactly what happens with my 1999 S Type - This was (I believe) a European spec - The delay is 15 Seconds
On my 2000 S Type, like the OP it goes off straight away, even after a full battery charge - The module stops responding to the fob after 10 or 15 minutes of being locked with the fob

This, in my experience is correct

Regards