13B-T engines have a weird system to shut down.. A vacuum switching valve will apply vacuum to a diaphragm, which will pull a lever and close a butterfly valve that will shut off the engine.
Some good tech with pictures of the components of this system on this thread.
forum.ih8mud.com
So, any one of several things could be wrong... not enough vacuum, possibly due to bad vacuum pump, or a bad brake or clutch booster, a bad vacuum line, or leaky vacuum storage tank, etc. Or, a bad Vacuum Switching Valve. Or a bad diaphragm. Or bad electrical connections to the vacuum switching valve. Or something mechanically wrong with the shut down butterfly. So many possibilities.
You can shut down by engine by dumping the clutch in 5th with the brake on (my preferred method). If you have any automatic, you can let it run out of fuel, or if your ar in a hurry, I suppose you could manually activate the diaphragm arm to close the butterfly valve.
This system can cause novice 13B-T owners many problems, and utterly stump non-13BT mechanics. It can cause various issues such as yours (Can't shut down), or other issues like "can't start the engine". Or the really frustrating one... engine shuts down when merging onto freeway. All are symptoms of this goofy system. The problems can come and go seemingly at random, and right in the middle of an otherwise peaceful drive. I've never seen a system like this on any other engine.
On one of my BJ74's, the whole system was bypassed by the frustrated previous owner unable to diagnose the issue, and he put in a pull cable to manual actuate the shutdown butterfly with a pull-lever on the dash.
Why can't they just have a fuel cut-off solenoid like a normal truck? sigh...