| Phill, it might be that one of the connectors has got a soaking and not the alarm??
With the ignition off and lights still being on, it could be a short in the switch itself or the connector from it in the loom.
The alarm would go off as it will be detecting a current drain.
Pull every connector you can get your hands on and spray with WD40 as a starter and see if it's cured. Also spray WD into the ignition lock itself. This will displace any water in the switch.
Call me if you're still struggling. | 
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