I used the wide velcro that is self adhesive on the back. Mine has been on around 4 years with no issues in my laundry room.
Mary: Velcro would be a good way to make the skirt "stick."
Self adhesive velcro would work well. One side on the sink the other on the skirt.
Not to necessarily stick to the sink, but you could use a tension curtain bar to put it between a counter that doesn't have door(s).
Maybe Velcro or maybe the Command Strips from 3M :)
Go to Michael’s crafts get a roll of Velcro put it around the sink we’re you want it to lay then eather stick it to skirt or sew it on then you could remove it to wash
I would use velcro Mary...put one part on sink and the other on the skirt then press them together to lock. Good luck
Did this years ago. I installed metal cup hooks on either side of the sink. Ran heavy duty elastic through the skirt and looped onto the cup hooks. In the front to keep from drooping down from the slick sink surface, I used Velcro dots, glued two to the sink and then on the skirt fabric. It worked well like that for a number of years before I remodeled. Easy to remove and wash when needed too.
Have you tried two way tape? Alternative, the Command products line makes some great sticky products now that may work.
I would use Velcro as shown here: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwi8ja3_u5PnAhVJPq0KHW41Am8QjRx6BAgBEAQ&url=https%3A%2F%2Fwww.onekingslane.com%2Flive-love-home%2Fskirted-sink%2F&psig=AOvVaw2_nh0Co2NkOSiOdLGihtI3&ust=1579654025125198