He has been gone for over a year so probably not around anymore.
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When I fist got my car, I changed over the front brakes. Only to find out the vibes were still there, they only went away after changing the rear rotors. The fronts seemed to have been good. So I’d check rears.

 

Did you buy OEM caliper? If not, where did you buy it from? Link please?

 

Rock Auto has a variety of aftermarket calipers available:
2012 JAGUAR XJ 5.0L V8 Caliper | RockAuto

Or if you want Jaguar parts, a dealership parts sales site like this (Suburban is one of several available):
Brake Components for 2012 Jaguar XJ | Suburban Auto Parts

Then there are some on-line suppliers like Autohaus AZ that offer genuine Jaguar and aftermarket parts.

 

Mine car is Jaguar 2013 xjl Portfolio 3.0
Currently installed parts are from Rock auto - I bought their most expensive caliper set. What I got was Jaguar brand rebuilt calipers, painted new, but within months the cover is fully rusted.
I dont want to spend $500 ea for jag OEM.
Autohauz AZ seems like a nice option - but they dont have jag calipers.

 

OEM