Andrew Quentert: According to Parts Lookup, there were three different versions of your tractor:
1. SLT 1554 with Command Engine
2. SLT 1554 with Courage Engine 2007 & before
3. SLT 1554 with Courage Engine 2008 & after
Parts Lookup, accessed from the button above, doesn't show a wiring diagram, and I don't find a wiring diagram for the SLT 1554 listed in the Wiring Diagram section on the Main Page of this forum.
I know that some of later IH tractors were wired with the PTO interlocked with the Reverse Switch and a Reverse Relay so that one could only mow going forward and NOT in reverse. It sounds to me like somehow the functionality got reversed on your tractor: maybe a plug got turned around.
I would start tracing things out from the PTO connector through to the PTO switch and then to the Ignition switch. Draw a diagram of the circuit as you go and compare it to diagrams you find listed in the Wiring Diagrams in this site until you understand how your circuit might work, then experiment until you get it working like you want it. But I'm comfortable diagnosing electrical circuits, I don't know if you are.
If you're not, another option is to contact the dealer and ask for a copy of the schematic for your tractor (which would be good to have in any case), be sure to have your model and serial number handy. Using the correct schematic, you should be able to trace the circuit and figure out what is not working correctly.
Just my thoughts . . .