screws in walls

Unscrew the light switch and the outlet from the wall and see if the wires all go up.

When you drill the hole, use one of those things (cant recall the name at the moment) that will only allow the drill bit to go 1/4 inch into the wall. That is about the thickness of the wall sheeting. That way, should there be something there, you will not puncture into it. I assume you are going to use anchors?

I had the same concern.
I used a very small drill bit and pushed it into the drill as far as it would go.
Then I took a piece of masking tape and wrapped it around the bit so that only about 1/4" of bit was exposed.
Drill until the tape touches the wall.
Now you have a nice little hole without piercing anything in the wall.
I went to the hardware store and got some shorter screws.
By the time it goes through the holder and into the wall there is hardly anything sticking through into the wall cavity.

It has been that way for 4 years and been fine.
I wouldn't want to put my weight on it or anything, but it seems to be doing fine.

You can put a small amount of wood glue on the threads when you screw them in if you want some extra holding power but you should be fine.

Bill

Use a stud finder. Most can discern between wood and plumbing/electrical. I know the walls in the trailer are thin, but it still works. I would want a TP holder mounted to at least one stud.

You might want to do what I do. I have mounted stuff all over the place in our trailer including exactly what you want to do, but I use a backing plate glued to the wall.
All of our trim is oak, so I use a piece of oak and route the edges to match the original stuff that came with the trailer. I also stain and polyurthane it to match.
Then I use brass screws just long enough so that they go through the backing plate and have about a 1/16" on ther back side.
I then cover the back with glue, (either gorilla or Elmers), and then force the screws into the wall. All these screws do is act like a clamp until the glue hardens. Then I screw my rack or whatever to that.
I am now on our second trailer where I use this method, and I have never had any of the many that I have done come off, and I have never had to worry about hitting wires.
Plus the backing plate adds a lot of nice finish.

Jack L

I have always used short wood screws to install towel racks, TP holders, etc into the luan walls with no drilling or anchors and have never had a problem with hitting plumbing, electrical, etc. Wood screws actually hold very well as long as they are not over tightened when first installed.

Have you considered 3M command strips??

Just drill a small hole to the point where it penetrates only the wall panel. Then take a straightened out paper clip and push it into the wall cavity and feel for items inside the wall. If you feel no resistance you can put in wood screws as far as your paper clip went into the wall. Any electrical wires will not be punctured unless they are forced into something solid inside. If you feel unsure about doing it this way you can use screws that have the points ground off, or if you have some,... use screws without sharp points on the business end.