A trick I have used, as a last resort... Drill a very tiny diameter pilot hole where you are planning to mount the towel rack. Drill it very shallow, just deep enough to go through the wallboard or paneling. Push a rigid piece of wire through the hole until you get the "thud" where it hits the outside wall. Now you know the longest screw you can safely use. If you decide not to go through with the installation, the hole should be tiny enough so it's not a problem to hide.
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