Lights no working except for red light on left side

You may have a bad starter relay. Have it checked out.

check for a problem ground for that light as it is grounding out through another light circuit

It's not just commercial aircraft. In the US (and most of the world), all aircraft will have those lights during night operations. [There are a few exceptions, such as aircraft without electrical systems - and yes, there are such things.]

The steady lights on the wings are called "position lights" (also called "navigation lights" or "anti-collision lights" or similar names). The one on the left wing tip is steady red (that's the left side, as you are sitting IN the aircraft). The one on the right side wing tip is green. There will normally also be a white tail position light (steady) on the tail.

In addition, most aircraft have strobe lights. A white light on each wingtip is common, as is a red strobe light on the tail or belly.

The purpose of the lights is two-fold (well, actually, the only REAL purpose is to help avoid collisions!). First, the strobe lights are there primarily to catch your attention. A flashing light is much easier to spot than a fixed light. The other lights are there to indicate direction. At night, it is very hard to quickly determine the direction of travel (left to right, away vs. straight at you, etc.). But by determining which colors are visible, you can quickly determine the orientation of the aircraft. Whelen (a primary producer of aircraft lighting) has a web page with nice diagrams: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0CDkQFjAG&url=http%3A%2F%2Fwww.whelen.com%2Fpb%2FAviation%2FSystem%2520Requirements%2FAnit-Collision%2520Systems.pdf&ei=v1wDVOv8E8nzgwSyroGABQ&usg=AFQjCNHZf7nhnmC_Mj0wp44-uLXBFB8gJA&sig2=h61HBbMEeD6fZA6vF9Czyw&bvm=bv.74115972,d.eXY

Hope that helps. [And the short answer to your question is - because one midair collision can ruin your whole day (or night)!]

Try the specified fuses in the under hood fuse center. they are common to blow.

One possibility is the rear axle isn't aligned so the rear wheel/tire runs true to the axis of the frame. This can be visible with the drive belt not running true on it's sprocket, pulling to one side of the pulley, rather than being about equal spacing on each side of the belt to each side of the pulley.
The other possibility is the rear wheel was removed, and the axle spacers weren't reinstalled in the correct position(s).
The axle spacers are different lengths, and are specific as far as which one goes on the left, which one goes on the right.

I don't believe it would be a bad ground for just one light. It could be a wire, a socket connector, or the bulb socket itself. See if the wire has power at the socket when signaling left, with key on. If there is power, probably a bad socket or connector. If no power, check for power coming from flasher-the wire going to front left, or driver's side. If you have power from the flasher, but nothing at the socket, the wire has probably broken.
Good luck.

It is broken, need to get a new one!

In order to check the tail-light fuse the lights must be on so you can check both sides of the fuse. It should be a 10 amp fuse(red). Good luck

Check it with a test light. White-ground, Yellow-left turn, Green-right turn, Brown-tailights. Check it on the truck first. There are seperate fuses for just the trailer wiring in the fuse box under the hood. The Blue and Red wires are for Trailer brakes, don't worry about those.

more likely the thermal coupling is u/s get new one fitted