Troubador, your problems could be related or not. I believe the instrument lights would be the easiest place to start/check since you could easily check for power at the park fuse, then the instrument lights fuse. A poor/bad/missing ground could cause any direct current electrical problem. The wipers share the same ground as the instrument lights.
Do no panel lights illuminate including climate control lamps and your transfer case shifter light? Hopefully you have pulled a couple of bulbs and confirmed they are good.
To add to ImpulseRocket, the hazard switch is part of the turn signal switch. What isn't making sense is only the drivers side hazards working. That would lead me to check passenger bulbs, then clean the sockets.
Safety first...no hot swapping of electrical components. Turn power OFF, then disconnect/connect cables/connectors/components.
For turn signals, equipment condition: ignition switch in "accessory", left turn signal on, hazards off - start from turn/bu fuse verify good and power exists there with multimeter or test light. If your D/S hazards are working as you mentioned, swap the hazard flasher and turn signal flasher to see if the same conditions exist (no turn signals and D/S hazards). I would also confirm if power is there using a multimeter or test light. From there, you need to chase the power to terminal "L" on the C156 connector to the turn/hazard switch assembly. Check to ensure it is securely connected first. If you have power at terminal "L", replace the turn/hazard switch assembly.
Question on wipers....do you have intermittent wipers?
I have had two clutch master cylinders leak onto my fuse box, some of the fuses disintegrated when I tried to remove them. I certainly cleaned my fuse box to get that mess off things and remove the gunk like exists on the C101 connector.