PARK fuse (10A). PARK fuse feed 12vdc to C269_B2. When light SW is set to PARK position, C269_R (Blue wire) becomes HOT (12vdc) and feeds your running lights.
I've seen that 502 Bad Gateway problem. Might mean nothing but sometimes when 'new items are posted' (auto update on activity window) 3 or 5 and sometimes up to 7 new items are shown (exact same post) at the same time. Screen REFRESH (F5) solves this and only leave the 1 new item.
No joke meant here. But just how do you tell someone their front grille is upside down or downside up without just saying it. We need a pinned TOPIC explaining how something like this can happen. That way it can be tagged and put in the post when this happens. MJ/XJ of the RENIX years have this problem. Two ways to put the same part on. Once again welcome to CC.
Hazard Flasher works, still I wonder about the Turn Flasher. I'd replace Turn Flasher, before digging into the T/S SW. Flasher is easy enough. I know you said LH T/S work while the RH don't.
As @Pete M mentioned above, odd that T/S will turn RH bulbs ON only without flashing. Do 4-way Hazard work? All 4 corners properly. Wonder if Turn Flasher is weak or just bad.
Is it possible you have a XJ Wagoneer Front Lighting Harness (FL) installed? Is there another connector, similar to this, on the other side? Wagoneer’s have dual beams, per side, for headlamps.
Disconnect all three wires from one side or the other. Determine if that still blow fuse. If not, reconnect that side and disconnect other side and do the same test on the other side. Checking for faulty fixture. Verify wiring while it all apart.
The ‘Bulb Check’ circuit used for Engine Coolant. Without gauge (bulb only), the bulb will light when engine is in CRANK, with gauge, gauge will peg (HOT) when engine is in CRANK.