Use a stud finder to find the wall studs . If you hit one, you could probably put two screws in vertically. I believe the wall studs are 2x2's so they should hold a small fan.
You maybe on to something with the fan under the mattress. Another option would be making a large "C" shaped stand from ply or 1xs the width of the fan's base and place lower section under under the mattress.
2013 26BH ghetto model w/ 4 plain rims and some rust
2001 Silverado 2500HD 6.0 gasser
I have a fever...and the only cure is more camping!