Thank you everyone for your suggestions. I have tried several things and think I have finally come up with a solution.
I used a tension type shower rod mounted in the tub. That was not practical because you always had to take the towels off to take a shower. :-(
I had an over the door towel rack that I have had for many years. Used it when we had company. It has 4 rods for towels. That didn't work either because our TT bathroom is so small I felt like I was squished between towels and the sink when I closed the bathroom door.
The light went off yesterday! I mounted 2 3M hooks above the toilet near the ceiling and have hung the over the door rack there. Eureka! It is not in the way and will hold our bath towels as well as hand towels and face cloths.
Again, thanks for the input everyone!