2003 Jaguar S-Type

The 6yr old battery on this car went down (whilst being driven) so bringing up lots of alarms. A new battery solved this but a problem still remains. After the car has been run with headlights on, when I switch off the ignition the headlights come on. Switch on the ignition & headlights go off -- this can be repeated many times. I leave the ignition on to protect the battery. After about 1 hour the fault clears & I can turn off the ignition without the lights coming on. This does not happen after every run but is getting frequent. On the last occasion, the next morning I found the new battery flat suggesting that ( for the 1st time) the fault reappeared in the night after initially clearing. This is driving me crazy! Can anybody HELP?