It is a 1999 GMC it only has 68,000 miles on it.
I work at a diesel shop. We
don't specialize in CAT. We don't have CAT specific software.
Those GMC Topkicks or Kodiaks or whatever they're called often don't have the round connector that most trucks have, they have the 19(?) pin DLC connector that cars have. They don't run on an OBDII protocol though. An automotive code reader doesn't work. So the crappy method we use to get the codes is to take our ancient Snap-On Modis, attach the Heavy-Duty serial bus converter thing (I've been drinking) to it, and stick a 19-pin DLC connector to the end of that. Yeah. Imagine how reliable this setup is.
Almost as reliable as these engines! Haha, just joking. Mostly.
In any case, you can probably rule out the HEUI pump simply because it starts and runs. I have a feeling that it is drawing air in from somewhere.
If I'm not mistaken, the fuel lines on these are made of a material similar to air brake tubing, and they have quick-release ends (a style often used on gasoline-powered Chevy and GMC vehicles of the same era). Is it cold where you live? Does cold weather aggravate the stalling problem? There are seals in the inside of the quick connect that can harden over time, allowing air to enter in small amounts. I've also seen these lines rub against the chassis, causing leaks. If there's signs of external fuel leakage at any of these quick connects, replace it. If it allows fuel to seep out, then air can be pulled in, too.
Since I'm not a CAT expert, I don't know if this is true for the 3126 or not, but I've seen more than one 3406 stall out because the square seal ring that comes with some fuel filters was not put on the threaded portion of the filter adapter. Since I think you'd want to change your fuel filters anyway, get some genuine CAT filters and see if they come with this seal ring or not. If they do, I think you'll always need one of these on the filter adapter threads, CAT filter or not.
The last thing that's an easyish check is the fuel return valve on the back of the cylinder head. This regulates fuel pressure in the head's fuel passages, and allows fuel to return to the tank. There is a spring loaded piston inside, and a check valve. You will need tiny snap ring pliers to take it apart. Mark this thing very carefully when you take it apart because it can go back together a couple of different ways (and look correct). In particular, there's an o-ring in there that acts like a valve seat, and when it disintegrates it can cause problems. Yours is questionable simply because of its age. Other debris in the fuel system can make the piston hang up, or the check valve can hang open. In either case, weird things happen. I don't think any of the parts are available separately. If something is fouled up, put a new one on.
I said easyish earlier; while this thing is simple, getting to it is not. I believe these trucks have a removable dogbox, so it's probably not that bad. The last one I went after had a huge console in the way. It was easier to remove the driveshaft and mash a small coworker in the space between the cab floor and the top of the transmission.
Edit: If you find that removing it was hard, getting the thing back on is even more difficult. The fuel return hose is made of that air brake tubing material, with a brass coupler nut. Super super super easy to cross-thread and mangle both the coupler nut and the brass fitting on the outlet of the valve if you don't get everything back in the same position. You'll see what I mean.
I'd be super critical of those fuel lines.
Edit: They aren't cheap though.
By the way, any other weird goings-on? Massive oil consumption with little smoke and no external leaks, for example? Is the fuel black? Sometimes the injector o-rings harden and start leaking. Sometimes fuel into the oil, sometimes the opposite. If you dig around upstairs and decide to adjust the valves (which should be done fairly often), do it with the engine dead cold and don't overtorque the adjustment locknuts. They are surprisingly easy to break. Don't go poking at the injector harness either, that thing gets extra crunchy.