engine keeps stalling

I had a similar problem with my XJR-S. It would run for 15 minutes then stall.
It turned out to be the ECU, after 15 minutes it reduces the idle RPM and emissions and cuts the engine out.
After I got a replacement all good.

Had the same problem with an XJS i owned in the past--sounds like it could be the crank position sensor.
Mine would start, run for about 100 yards then die, wait for half an hour then it would start and run for another 100 yards etc etc.
Hope you get it sorted

i have a 1988 v12 5.3 ltr convertible , the engine keeps stalling and then turns over and wont start then it starts an hour later but drive a mile or 2 and stalls again , i thought it was a blocked fuel filter but its not that and the fuel pump is fine , there is a spark at the plugs and all fuel getting through i havent a clue where to start it runs then cuts out , wait abit and runs again then cuts out wait abit then runs and then keeps doing this