Umbrella holder?

I can't comment as to whether or not it's useful for that purpise as I have the use of both of my arms. My wrists are often in splints though, I can't hold up anything heavy like an umbrella and I mostly have only my left arm free when moving around as I control my powerchair with my right thumb.

For me personally, a simple poncho and a pair of wellies does the job without needing to carry an umbrella or anything to attach it to. I don't tend to buy things that are designed specifically for disabled people as there is usually a higher price tag attached and can be clinical looking. I don't have a wheelchair poncho, just a Joules one that happens to cover my chair. I've also found that when you substitute the word wheelchair for pram or buggy, you can often find the exact thing you're looking for but cheaper/more aesthetically pleasing.

So I would say that after functionality, when I look for aides the main things I look at are price and if they look nice.

As far as functionality goes - i have in the past attempted to attach various things to the back of my chair... mostly a large umbrella, and crutches. Attaching an umbrella to a backpack strap doesn't seem all that different to trying to attach it to a chair. When I recall times I've tried "holders" in the past two things stand to me.

First is that the best ones fastened the item to be held in two places. The worst ones tried to balance all of the weight in one place. They just loosen with the swaying movement and become annoying/hazardous. If I needed an umbrella holder I would design it so it holds the umbrella at two separate places along the length.

The second thing is that it must be secure but easily removable. I had some crutch holders that were adjustable and very secure but it took me ten minutes to unscrew the things. The simplest and best ones I had were strips of strong velcro. An umbrella is something you might want to put away easily so I would bear that in mind.

Good luck with your idea.