As of right now we have no lights on the right half of the instruments,
This will require opening the instrument cluster and examining why some gauge lights are not working. All lights in the gauge cluster are fed from power on pin 24.
no neutral or gear numbers,
This is not a correct statement, isn't it. You stated earlier that you have "4" and "5" displayed. I'll hazard a guess that your gear shifts produce the following sequence:
Selected gear = displayed gear #
1 = 5
N = 4
2 = 6 [BLANK DISPLAY]
3 = 7 [BLANK DISPLAY]
4 = 4
5 = 5
Since the display can't show "6" and "7", a blank is displayed. This response corresponds to your previously reported symptoms (i.e. "It displays only 4 and 5"). If the Yellow/White wire was not making contact at the connector, it would appear stuck open at the gear indicator circuit. So the above gears would be registered. Check continuity in the harness connector for the TGPI under the right battery cover and at pins 2 at the cluster.
no running lights on the right but turn signals OK.
There are no running lights in the turn signal indicators on an RT. If 1157 bulbs are fitted, this might be an electrical modification by the PO.
ABS fault (which continued when we had the bike running the other day).
Troubleshoot the electrical problems, then troubleshoot the ABS.
Also no parking light although the bulb appears to be good under magnification,
Parking light is fed from fuse #2 directly. The wiring passes through the BMU connector, but it is essentially a direct link from the ignition switch to the bulb socket. If the PO fitted running lights as a modification, then maybe he tapped into the grey or grey/white wire in the relay box, or at the ignition switch. If so, you've got to troubleshoot the PO's mods first.
no brake lights.
The BMU and brake switches are fed from fuse #1 so blown fuse means no BMU and no brakes.
Fuses do not blow when key is put in Park.
...but they blow when you put the ignition into the "ON" position??