I recently bought my wife a 2002 XK8 with 30,000 miles on the little beauty. I got her for a steal because the previous owner couldn’t get to roof to lower, so I did some investigating. I discovered it would work if I pressed a little switch manually while depressing the roof switch, however the rear windows do not show any sign of working. I am including a video link to show the process.
Also, if anyone can tell me what plugs into the yellow connectors shown in the separate pictures, I will be eternally grateful. On a side note, what do you Brits think about Ted Lasso?
Cheers and thanks!

 

Here is video of relay in question

 

I believe the yellow connector is for the roof console light and switches.

When you hit the "roof down" switch, the BCM (Body control module) will send a roof down request to the Security and lock control module. The security module will then send power to the rear quarter window down relay for 3 seconds and the chime will give a beep to warn you that the roof are about to open. If none of those are happening the problem is before the roof relays and hydraulics.

Here you can download the Technical bulletin:
501-11

 

there are many videos on youtube how to manually open the roof. the xk8 has a opening sequence starting with the windows dropping.
there is a way to bridge the power of the rear windows in the relais box (cant find the instructions atm).

in the top you have light switches.

btw do you have a airbag fault (light on)? 😅