No other relays in a 99. At least not stock. Hopefully there isn't an unknown aftermarket remote starter causing this. Look at the wiring coming out of the ignition switch. Lots of large gauge wires from a 2X4" "rectangle" connector to the left side of the steering column. If there are splices in these wires, there is some aftermarket system installed. Look at the red/lt blu wire. This is the START circuit. If it has been cut in half, and wires spliced to the ends, this could be the problem. If you don't use (or even know your truck has a remote starter) splice the two ends of the factory red/lt blue wire back together, and that should be the end of it.
If an inspection doesn't reveal any aftermarket installations at the Ignition Switch, try this:
In the underhood fuse box:
Remove Maxi fuse #20, 50Amp (red). This is the feed to the IGN switch START circuit. If this makes it stop, it's the IGN switch. If not:
Remove Maxi fuse
#21 , 50Amp (red). This is the other feed to the IGN switch. If the voltage goes away at the little connector with either of these Maxi's removed, the voltage is coming from the IGN switch.
If #20 and
#21 have no effect, remove Maxi fuse
#22 , 50Amp (red). This is the feed to the under dash fusebox / GEM / junction box. If the voltage at the little connector now goes away, it's something to do with the fuse box, OR an aftermarket system being fed from this fuse box.
IF
#22 makes it stop, I would suggest taking it to a 12Volt specialist. Let someone with some experience and knowledge take a look, as it can get expensive and complicated if one is just guessing at this point.
You can also try removing Fuse#20 in the UNDERDASH fuse box (#22 Maxi installed). If there is now no power at the little connector for the solenoid, this is another test that the voltage is at the ignition switch or something attached to the red/lt blue wire at the switch.
If there IS power at the little connector with under dash #20 fuse removed, the problem is the fuse box junction box has a short to voltage, or the GEM has shorted this circuit to voltage. (I think this is highly unlikely. The GEM uses this circuit as an input that the starter is engaged. It does not "control" the starter itself.) Again, take it to a specialist.
The GEM is on the rear of the fuse box. It is pretty fussy to access or remove. Again, I doubt it's the GEM itself. Possibly the traces within the fuse box going to it.
Is your truck 4X4 shift on the fly, or 2WD or floor-shift 4X4. The GEM is bigger / different for the shift on the fly T-case as it contains the electronics for controlling the T-case.
You're making progress figuring this out. Leave the little connector off when the truck is un attended. Save your batteries and starter.