Three wire as shown would normally have turn signals and brake lights but no taillights.
I would start by using a small jumper wire to see what functions are working on the trailer. Connect jumper to a good battery, use jumper cables to attach battery ground to rig. Then connect positive jumper lead to yellow and then green to see what actually works.
Follow black wire to see if it operates a function or is the ground.
You should convert the trailer to a standard four wire.
Bud
USAF Retired
Pace Arrow
2003 Chev Ice Road Tracker