A very interesting starting problem
A couple months back my 98 f150 triton v8 stopped starting with the key altogether, since then I've replaced the battery, starter, starter solenoid, and ignition cylinder, checked all my cables, and still no start, I hear a click, but nothing else, it'll start with the key in the on position and if the starter or starter solenoid are jumped manually, my buddy thinks it maybe a car alarm feature from loctronrics but I doubt it highly.
If you do indeed have a locktronic in your truck that could certainly be the issue. They are not known for being very reliable. I'd check the fuse/relasy that is used with it before bypassing or removing all together.
Doesn't do much good since a thief can start the truck the same way you have...
Doesn't do much good since a thief can start the truck the same way you have...
I've looked at all fuses and relays, and replaced half of them on just good principle, I don't know how to go about removing the stupid loctronic, or if that'll fix it at all. I'm half temped to run a couple wire from my solenoid to a switch in the cab.

