My 1998 jaguar xj8, when in the 'auto' headlights setting when i put right turn signal on, my headlights flash along with the turn signal

 

You may have a bit more joy in the X308 part of the site,

https://www.jaguarforums.com/forum/xj-xj8-xjr-x308-27/

I never had any trouble with the auto headlights on my X308, have you tried swapping the bulbs just in case there's a dodgy connection?

I did get a pair of bulbs (£6) when one went out and it was a straightforward matter to change them, a far cry from the expense of my new Jaag when its all singing/dancing Xenon ones go 'pop'.