Texas trailer light regulation question

Just a question for you Texas folks about trailer lighting. I am thinking about changing the taillights on the trailer to some surface mounts and get rid of those ugly, hideous monsters sticking out back (also Planning on replacing the amber side marker with a tear shaped one as well) Currently I am using the original that came with the trailer, which are stop/turn/ taillight combos.
Here is a picture of what I have

However when I convert to the flush mount, I will lose the side marker and plate light built into the unit. I can install a new plate light, but will I have to install a new side marker light for the rear (red)? And if so will if also have it indicate a turn? Anyone know the regulations?
Here is a picture of what I have


However when I convert to the flush mount, I will lose the side marker and plate light built into the unit. I can install a new plate light, but will I have to install a new side marker light for the rear (red)? And if so will if also have it indicate a turn? Anyone know the regulations?