Anti-theft, immobilizer, battery and Stabi-Trak lights turned on?

Are those lights on at initial start or do you have to drive it a while then they come on. At which point in the cycle of lights does the engine shut off?

From the description it sounds like a wiring harness or PCM issue that is causing it.
Does the theft light stay on solid when you start the truck or does it work normally until the problem happens?
Being essentially a GM Trailblazer with a Saab badge it likely has the same harness issues as it's siblings.
I would start by having a scan tool that can watch the network on it connected up and drive it until it acts up, then look to see what the tool shows, if it is the CAN network dropping out to the dash or to one of the other modules it will usually show up.
https://www.2carpros.com/articles/can-scan-controller-area-network-easy

Those codes are all network communication failure codes.
U1064 - Lost Communication With Body Control Module
U1192 - Lost Communication With Vehicle Theft Deterrent
This code though suggests where the issue is
U1301 - Class 2 Data Link High
That one shows that at the time of the failure the data line is becoming shorted to battery voltage for at least 3 seconds, that will stop the network from operating and set the other errors because of the short.
The hard part will be that this condition is an intermittent one so testing for it is going to involve putting an oscilloscope or a data monitor on the class 2 data line at the data link connector then monitoring that signal as the fault happens.

Has anything been modified in this truck like an aftermarket radio? Or a tracking device that connects to the OBD port?

The attached image is the data lines on that truck. Everything that says class 2 data is a suspect. It could be internal to a module or simply a wire rubbing in a door.
To narrow it down will require finding the two splice packs shown. I suggest starting with the one under the rear seat. Unplugging it and then drive around and see if the condition still happens. If it doesn't then look at the items on that side of the network first for a problem.
If you unplug that splice pack and it still happens then you will need to look at the various data modules on the other splice pack. To test those you can do somewhat the same test, namely find that splice pack under the dash and unplug it while watching the network, start the truck up and see if the problem still happens, if it does then look at the theft deterrent module for the problem as it would be the only module still connected to the powertrain control module with that splice pack disconnected. If it doesn't still happen it will be a bit harder. You would need to go to the splice pack connector and remove one of the data line pins from the connector then test drive the truck for failure. This would be repeated for each data line pin. However as you are getting the codes for theft deterrent and stability, I would suspect it is either the theft module or the brake control module. That is causing the problem.

Okay, as a first test disconnect the radio, I have seen ones that link to the data systems cause problems, either in the radio or in the wiring to them, It may not be the cause but it's an easy item to test before digging deeper.
The data line sends signals through all of the connected systems, so a failure on any of them could result in the engine shutting off as it prevents the communication. The only good thing is that vehicle has relatively few modules to test, unlike some newer vehicles that have 3 or 4 different networks and 30 or more modules to test.

No rush, we'll be here. I know how this testing can take a bit, especially on an intermittent issue. I've worked on some that took a week or more before the problem would happen while I had the vehicle.
One thing that might make it faster would be to test it and when it fails, don't turn off the key or disconnect anything immediately. You might be lucky and the item causing the problem will "stay broken" if the power stays on and then a scope would show it easily when you started unplugging things.

Good to hear you found the issue. Unfortunately it's a common thing these days with the aftermarket items that connect to the cars networks. The issue is that there are different network communication protocols used in different brands and models and the aftermarket folks try to use a one size fit's all approach. The results vary depending on what else the network controls. On some it's just simple things like you lose the seat memory or the chimes stop working, on others it can lock up the communication buss and cause real damage.
You are welcome, please return anytime with your automotive questions, let others know about us.