Blinker issue, solid light

1994 Country, all stock

My right turn signal is not working correctly. Here are the facts...

- When I turn it on, I get a solid right turn signal light on the dash and it does not blink
- With the headlights on, I get the same result as above, but the right turn signal light on my dash stays on
- Hazard lights work normally
- Left turn signal is working normally

I have replaced the right, front socket with an OEM part from a pick-n-pull. I have also replaced the right front and rear bulbs and checked the ground behind the spare tire corner panel. Issue persists.

Any ideas? Thanks in advance!

Sounds like a grounding issue. Make sure the ground wire to the headlight is getting a good ground, and make sure the perimeter of the park/turn signal bulb is likewise getting a good ground, Typically if a turn signal flasher works one direction, but not the other, it'll mean a bulb is not working, therefore not drawing enough current to activate the 'blinker' switch inside the little can. The headlight may be trying to ground through the little bulb, hence the dash indicator glowing. Check all the grounds with a meter set to read resistance, to see where the problem is.

From 1994 Jeep Service Manual, posted under the copyright "Fair Use" rule:

Remove turn flasher, light blue can, located in
fuse block.
(5) Turn ignition switch to ACCESSORY. Check
for battery voltage at cavity on left (closest to hazard
flasher can). If OK, go to next step. If not, repair
open circuit in wiring between turn flasher and #4
fuse.
(6) Turn ignition switch to ACCESSORY. Move
turn signal lever up or down. Replace turn flasher
with known good flasher. The lamps should flash. If
not, replace original flasher and go to next step.

Thanks for the replies, y'all. I checked all the grounds and everything was testing normally. Turns out I neglected to inspect the little, amber indicator bulb in the front. When I pulled it to test the ground in the socket the bulb fell apart in my hands! Replaced it and bingo... let there be (flashing) light.

Thanks for all your help!