Hi David .
This is a tricky system to check with out the Jag or top level diagnostic scan tools to check the
alarm activation list ,this tells you which switch is nor closing fully and activating the alarm.
Most common is the bonnet switch and then the drivers door ,you could check this first if the inner lights are on then most likely a bad door switch if not on could be the boot or bonnet .
If all these are okay then a possible module issue .but as said a good scan tool at your local jag shop or dealer will be able to track
this down pretty fast .
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This way i can get back to you or suggest another expert if needed.
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Kind regards Greg.