When turning on the headlight switch, the right passenger side blinker stays solid and does not work?

Yep, this happens when the right passenger side blinker has a bad ground or the bulb socket is melted allowing a back feed condition when the headlight is on, lets remove the right rear blinker assembly to check it out here are the instructions in the diagrams below. Also, I have included the blinker wiring diagrams so you can see how the system works.

This guide can help as well:

https://www.2carpros.com/articles/turn-signals-not-working-blinker

Check out the diagrams. (Below) Let us know what happens and please upload pictures or videos of the problem.