https://www.ownerinfo.jaguar.com/doc.../proc/G1853098
'Headlight courtesy delay operates whenever the lighting control is in the AUTO position and the ignition is switched off. The headlights remain illuminated for up to 4 minutes. Press the smart key's headlight button to switch the courtesy lights off.'
I suspect that the time-delay can be altered from the 'Vehicle Settings' area of the 'Instrument Panel Menu'. Perhaps a radical solution: you could turn off the 'Auto' lights function on the stalk...
Good luck!