Avoid generational distinctions to focus on collective experiences
It's tiresome to discuss different generations in terms of broad characteristics, and in the context of mentorship, those distinctions might not be very relevant. Rather than creating a clever, instrumental way to contrive a symbiotic interaction to refer to as "mentorship," why not focus on creating collective experiences that give a common center between a 15 year-old and a 75 year-old?
Maybe this means discussing a film, or watching theater together, or something in the outdoors. It could be cooking together, or having young people take oral histories from their elderly friends, or map-making (I call for map-making!). These things are more about real interpersonal experiences rather than tropes of traits.
The chief prompt of this contribution is to avoid what some Milennials would cite as important for buy-in, and what too many Xers and above seem to take the bait for—namely, cheesy marketing that smacks of a contrived initiative. I really wonder if the best way to mentor up is to allow Milennials and seniors to have mutual experiences that they would never have otherwise outside of the context of family engagements.
Seniors aren't just physically isolate, but culturally and socially isolated as well. The problem is exacerbated by a lack of accessible options for daily activity. It's a positive feedback loop in which isolation breeds aloneness, which only promotes further debilitation psychologically and physically. I can't back this up by data, just observational and first-hand experience. I once repaired a house for a very elderly couple who were physically handicapped to boot. The husband was partly blinded after a stroke, but he was a furniture maker for years and years, and still had a creeky table saw in the basement. We got it out, and despite my assumption that he couldn't do anything but sit inside, walk to the kitchen, and maybe stand on the porch, he helped me strip wood siding for his house. This gave us an opportunity to connect culturally, socially, and physically through our work in a way that fundamentally changed the dynamic of our relationship.
No quirky logo or marketing schnazz could accomplish what a simple collective experience can. As a first-wave Milennial, I can assure you that it is the younger people who will benefit from those sorts of experiences more than they know how to imagine.