Does it physically go into gear and does it drive in forward or reverse?
Not saying you should jump into these parts first, cause the first thing you should do is what retro recommended above, but one thing to keep in mind is that on these Hondamatic Rubicons, the angle sensor is only used for the swash plate angle. It has nothing to do with the gear position of the subtransmission (R-N-H-L). There are gear position switches for that. But since they are all acting up I'm thinking it is harness or connection related like retro says. If it were an individual position showing the '--', then I'd say it was that specific switch.
Edit: looking at the parts diagram I could be wrong, 400AT hondamatic uses the switches I mentioned. Looking for equivalent for the Rubicon, need to verify.
Edit 2: look at the "switch assy, change" here:
https://www.partzilla.com/catalog/honda/atv/2013/trx500fpa-ac-fourtrax-rubicon/rear-crankcase-cover that would be the part that reads what gear to display for the subtransmission position. Check it's connector out and wire condition before replacing it. I don't have a copy of this service manual, but there should be a specific section to address this.