Any suggestions on how to keep a mostly deaf, blind and immobile mother occupied?

All of the above depends on her level of blindness and deafness. You can go to a low vision store online and see what products she might benefit from. My mother has AMD and is EXTREMELY hard of hearing. We've have gotten most of the aids for the blind, lights, large print books, free audio books for the blind, etc. She wanted to be able to read but couldn't and didn't enjoy listening to others read the story. Her vision is so poor that she can no longer use these things or had no interest in some of them. Her hearing is so poor that she can't listen to the TV even with the best hearing aids. Any aids you come up with has to be something she is interested in and WILLING to learn. Without their cooperation none of the above ideas will work. My mother is one of the best in the world, but she wants what she had 10-15 years ago and if she can't have that she really isn't interested in more. She's been willing to do the enhanced lights for low vision, etc. But beyond that there is not much she found she is able to benefit from. Her age 96 is also against her. It's hard to change at that age and as one of the comments above stated, she's tired. She also doesn't have the ability anymore to learn anything that leans to the memory and techie side. So, the best you can do is be available to talk and if she is allowed to walk around, that does help. Depending on her age she may also tire easily and likes to rest. Another thought I just had was if she can see close up how would she do with some crafts, such as beads, etc to work with? Good luck, don't let guilt get you down. Sometimes all you can do and what you want to do for them are incompatible.

She can only see images up close? Get her an Oculus VR headset.

Go to the website Helen Keller National center for deaf blind youth and adults. They will probably have other ideas. When I think of Helen Keller, she learned through the touch and there may be things she can do through touching- sorting.