I'm hoping to have a more complete article on this topic next later this year. For now, here are my thoughts and an experience.
Involving an elderly person in your group might require finding someone to give them a ride, adapting your facilitation style to make sure they stay included, and choosing some topics that allow them to express their current life concerns and issues.
Starting a group for the elderly might require choosing an accessible location, meeting in the daytime, and finding topics for all of the sessions that focus on the issues most important to the elderly, as well as adapting your facilitation style and getting rides for some members,
And now, my story. There is an elderly person in the group I currently lead. Let's call her Harriet. A family member usually brings her to meetings and participates in the group as well. When the family member is not available, someone else gives her a ride. For the first six meetings, Harriet participated in check-in, but then tended to "doze off" during the discussion and it was getting progressively more obvious. My co-leader and I just let that happen. After the sixth meeting, I decided that I was going to keep her engaged in the discussion topic, whether I was leading the session or not. Simple enough. I was just going to ask her a question as she was falling asleep. For the last two meetings, she has not slept and has participated actively, but she did it herself. I haven't had to ask her a question yet. Serendipity, grace, mystery---they all happen in covenant group meetings.