....there is a product out there called Miracle Putty (I think its called). Its one of those 'as seen on T.V.' (??) advertized by Billy Maze???
It looks like it might work, but the idea of automotive double sided tape sounds better and easier to work with. This tape is w i d e l y used to adhere trim pieces to auto bodys and I'm sure it has many other used.
I doubt very much that rolling duc tape over onto itself would grip to any thing too much, a roll of towel alone is fairly weighty ....then factor in the weight
of the holder itself...