I recently bought an 89 XJS. When I filled it up with gas, I only got 3 gallons in it until it shut off. The car still showed half tank, tried another gas station and same thing a few days later. What could possibly be the problem?
For record the car has had a engine swap to a ZZ502 and TH400 trans.
Your fuel sender may be bad. The floats age and begin to sink over time.
Not a difficult part to replace….you just need to do it when you’re at about a 1/4 tank.
Either bad fuel sender, or your tank venting system is not working.
A good general purpose fuel treatment/ marval mystery oil just may “zap the crud” on the in tank rheostat. Can’t really hurt- injectors might even appreciate it.
If your tank venting system is not working, as Greg suggested, then your tank could be partially collapsed, and the float for your gauge might be hanging up.
What causes a tank to collapse?
Sounds like what Superblack did when I tried to put gas in her after buying her (and the only time to date - 
)
Same question, and I hope Jag corrected that issue (clogged vent?) by the '92 face-lift year. 
I’d hate to think that’s what’s wrong with Superblack.
Welcome to the forum, KS. 
btw, what is a “ZZ502” engine? 
Is that the magic level, VK? One caveat on that is that if your sender is bad, you may THINK you have less than 1/4 tank of gas in it until you go to remove the sender cover plate. 
I had assured my ex roomate-tech bud that he could remove the plate on Superblack so we could eyeball her sender, and in reality she apparently had a bit more gas in the tank that what the (faulty) gauge/sender showed, so as soon as he started to take the plate off out came pouring fuel. 
He was quickly able to twist it back on, but not before creating a mess in the boot that needed to be carefully cleaned up. 
So, beware of that possible “Catch 22”. I think what we’ve planned to do next time when we go to r/r the sender is to first pump all the fuel out of the tank with one of those hand pump siphon hose gizmos.
btw, speaking of fuel senders, it looks like from the Classic Parts site that Jag apparently changed the design on those things 2 or 3 times, not inc. the different versions for “coupe” and “convertible” … 
and possibly there was one design unique to just the '92 V-12s. Hence why I have been having a hard time finding even a used one for that MY. 
Is that in fact correct?
8.2L V8 Chevy Engine
As fuel is removed from the tank, with the engine running, air needs to take its place. If the vent system is not allowing that to happen, then the walls of the tank get “sucked in” enough for the float to hang up.
That is why you may get a “whoosh” sound when taking off the gas cap. (Positive or negative.)
Well Superblue almost always has a bit of a “woosh” whenever I take her cap off, and has been that way since I have had her (25,000 miles / 5 years). I wondered whether that is normal for the 4.0s …
Not normal. You should not have a woosh sound when opening fuel cap. I suspect the Rochester valve is bad. Maybe the hoses connecting that valve to the charcoal canister is blocked.
I’m not sure what’s needed for your MY, in terms of a fuel sender.
yep, i had a whoosh when i first bought car. Replaced Rochester valve. No whoosh since.
$30 part, about 30 minutes of work.
Do you have a link for that part?
Search for - AC Delco 214-552
And Where is it located?
Depends on your year, mine is 88, which is I think same for most:
Remove front/left wheel.
Remove front area of plastic wheel well cover (a few screws)
You should see charcoal canister with tons of hoses everywhere.
Rochester valve is somewhere in there on a hose going back to tank, pretty easy to get to.