Screen readers and mouse

I'm building an accessible tooltip — my first dive into the world of accessibility. It is shown next to an input and right now I'm thinking about how to show them to users with disabilities. The design does not allow to show it on focus so I was thinking, do screen reader users touch/have mouse at all? My idea is to hook for the first mousemove event and switch mode of tooltips to show on hover, and if no mousemove ever happened — it would show on focus. But I have nobody who could tell me about his disability experience so I was hoping if people here have knowledge on screen reader users patterns.