first of all , welcome
secondly , congratulations on buying an XJS , and a V12 at that ( pictures are required......its the law

)
your problem could be several things, and i wouldn't drive the car again until you have sorted the issue, as overheating can twist the heads on the V12 , and then its a coffee table candidate,
the engine has so much coolant it requires an expansion tank , and also an overflow tank that acts as an atmospheric recovery bottle ( the engine sucks back from this when cooling ) , this system needs to be perfect for correct operation
also turn the inside heater to on and hot, to ensure full coolant flow round every system ,
is the coolant to the correct level >
this is done using the two pressure caps and filling in a particular order,
remove both filler caps , one at the front of the engine, and one on the expansion bottle tank on the left inner wing , using the correct coolant ( but water will suffice for testing ) fill the system from the front engine cap , do this until the coolant runs out of the other cap on the wing , make sure you do this on level ground. then fit the cap on the wing , and then continue to fill the front engine pipe until the level is just below the cap , then fit this cap ,
your system is now primed,
you can start the engine, and let it tick over , if working correctly , it will start at about 1200-1500 revs then drop down to 750 revs , this is normal , if it hunts, then thats another problem we can sort later,
the coolant will now be being pumped round the system , with the mechanical thermostat shut , the coolant will bypass the radiator until the thermostat lets it through ,
let it run for a few mins, just to distribute the coolant,
turn off the engine and then check the front filler tube again , if the level is low, then top it up , you can't put in too much as it will overflow automatically to the overflow tank and out onto the floor behind the passenger front wheel ,
keep doing this process until your confident that the coolant level is full as designed,
btw , the level sensor is mounted on the left wing tank , this is what brings on the dash light if the tank is dry ,
other things to check for is the pump belt on the front of the engine, as the water pump is belt driven , ensure the pump pulley is spinning when running, keep your fingers clear though !!
and then the thermostats ( mechanical ) need to be proven , the radiator should get hot during this , but they could be stuck , i would change them anyway , but prove the system first
then i would run the car up to temperature while ticking over , monitoring the temperature and listening out for the fans to kick in ,
if you have an original viscous fitting fan behind the rad, check that it spins freely when cold without the engine running, and is grabbing when hot ( right after you turn off the engine, )if not then this has failed and its time to convert to full electric cooling like i have done
as for steam out the exhaust, this is normal for the first five mins of starting a V12, but it should then stop
if you do indeed have steam , then that means one or both head gaskets have failed into the cylinders, and require immediate work to stop complete failure of the engine
good luck
BB