Hi Chris---I also welcome you to the club your 1989 XJ40 sounds very interesting it would
be nice to see a photo if you could plus the 2011 XF you have 2 great cars there ??
Battery sounds good but as I said have you checked the battery to earth it could look good but if I was you I would disconnect from
body of car and reconnect making sure its OK ???
To me it still points to a battery problem or battery connection perhaps the earth point ??? and did you make sure to put the battery on that Jaguar recommend ???