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Machine runs off of oil pressure, but that hydrostat turns gears, and the gears seem to be your problem.  Before you start pulling things apart, let's check the easy stuff first.   And yes, you need the wires on those brake switches.  That's what allows the engine to start in gear.  It will only do so when the brake is applied.

Thanks @jeepwm69!  This is a great start, I'm really hoping not to have to tear any further into this machine but maybe I'll just plan on pulling the back cover off tomorrow.  I tried turning the engine over with the right lever pulled and that didn't help, also with the pull cord.  I noticed that under the right brake lever two wires that hook in and one was not connected, is that a neutral safety switch or something?  I might just keep this thing jacked up on stands and try and get it running as a starting point.  I'm not too mechanically skilled just know the basics, so I'm hoping that these initial issues aren't all related and causing the thing not to even want to run.    How much oil is going to leak out the back cover when I pop it off?  I guess I'm basically looking to see if the shift drum is free and not jammed up, and it's engaged in a gear (doubt I will know what gear if it is).  Does these run off oil pressure or just a straight up mechanical operation?  

@rich250rracer -- You are right -- there is nothing wrong with the gear position switch -- there is NO hot voltage on the gear position switch -- all 7 wires are grounded one at a time as you go through the gears.

Gear indicator on the dash indicates every gear, so I don’t think there is one.

Well the shifter you use on the left side of the tank shifts N, L, D, and R.  That's it.  All of those associated gears are under the rear engine cover.   The actual transmission on these Rubicons is a hydrostatic unit, so it runs off of oil pressure.  Yes, there is a shift motor, but all it does is move the swash plate on the hydrostatic, so what you have going on is something either in the mechanical linkage between the shift knob and the engine, or something under the rear engine cover in the shift drum and associated drive gears.   There are some pics in this thread.   Third post down shows the gears on the back of the engine.  When you shift from N to D, L, or R, that shift drum turns, and moves the shift forks, which engage the appropriate gear.     This schematic shows the shift shaft and how it engages that shift drum.   https://www.partzilla.com/catalog/honda/atv/2007/trx500fga-2a/gearshift-fork-gearshift-drum   So the shifter turns that shaft, which runs all the way through the engine and turns the drum under the rear engine cover.   I actually have to pull the rear cover back off of one of mine.  I went through the engine and must not have gotten something together quite right as I only have 3 gear positions and when the machine shows Neutral it tries to move forward.  I think I must have gotten a gear backwards under that back cover.     But do you understand the general concept now?  You move shifter, shifter linkage turns that shaft in the schematic, which turns the shift drum on the back of the engine.  The shift drum moves the shift forks, and makes the proper gears engage each other.