How to connect this wiring?

I use solder less crimp (butt) connectors, (usually blue) auto parts stores, wally world etc. sells them plus I use shrink tubing over the splice and it stays sealed from water etc.

Do your tail lights (and other lights) work when hooked up?

From the picture it appears you have two green wires coming from the trailer, one connected to the connector green wire and one connected to the connector brown wire. If that is the case I would guess the "repair place" added new (green) wires and used one to connect the tail lights to the brown connector wire. Bad brown wire somewhere under the trailer maybe? If that is the case, the loose brown wire is not needed. Look under the trailer and trace that loose brown wire. Likely you will find the other end not connected either.

Yep, the brown wires control each of your rear running lights (thus 2 wires). My open trailer is wired the same way.

You would splice the brown to the brown with a Blue butt connector using properly sized crimper.
Do not use the ones in the previous post. Blue butt connectors
I fill the butt connector prior to crimping with electrical grease.

Use a wire splice to connect all the brown wires together.
http://www.amazon.com/Solderless-Wire-Quick-Splice-Connector/dp/B009O0NZ6S/ref=sr_1_7?ie=UTF8&qid=1461602329&sr=8-7&keywords=16+gauge+wire+splice

Thanks. I can take a closer picture this evening. Which should make it more clear. My concern is that when the repair place connected the cables they all are paired up so this cable needs to be combined with another cable. A better picture will help clarify. Unfortunetly, the repair place was out of town so I can't take it back to them.
Thanks!

Etrailer.com has alot of wiring info for the trailers. Great source for all tings things trailers...

Maybe they can help you confirm tings...

Roy Ken

Usually a flat 4 goes like this:

Green=Right turn and stop
Yellow=Left turn and stop
Brown=Taillights
White=Ground

http://www.etrailer.com/instructions

I see the picture.

Unfortunately, the number of wires and connections aren't discernible.

Standard 4 wire trailer connections are depicted here