Switching sides while climbing walls

Hello there! I am currently making a wall climbing system. Everything seems great so far, but I want to take it further another step, how would I switch sides while climbing walls ?.
Here is my current system: https://gyazo.com/27cf5abb8eb6389129005997d9c43396
Here is the feature that I desire: https://gyazo.com/69d6a93c0a4666399b184df8df5071f2
I have looked through other posts and even some open sources materials, but it does not seem to work at least for me. I tried using ray, casted it to the right / left vectors of the player, but it will only function correctly when a part is right beside them. Is there any way I can make it so that the player automatically switches sides ?

Any help is appreciated!