My brain is fried on this. It'll start up and run for about a minute or two, and it dies like I turned the key off. But it'll start up again and then it's the same thing over and over again. I don't know what to do or where to look first.

 

Have you verified spark, fuel drop outs during a stall?

 

Since we don't know if it is fuel or ign related all we can do is attempt to isolate each system.

I would start with the ign system because if it were fuel it most likely would drop RPM and eventually quit.
A lot of simple checks can be made with a test lite although you have to be careful on newer vehicles, that don't like test lite checks lol.
What you might want to do is hook up the test lite to show if and when power is supplied by the ign sw to the coil . If the lite does out and the engine stops , problem is involving ign sw. If it stays on and the engine quits now you need to see if the ign module is losing the signal to the coil to ground it and create the spark.
Let's see what we get here before going further.