Migration assistant not finding time machine

A little more perseverance and I could have avoided posting this question.

I found a solution that worked for me. Migration Assistant had found my other laptop on the network and offered that as the only source for copying data. I did not highlight that. Instead, with nothing selected, I clicked on Continue. That brought up a box asking for the password for the encrypted back up - that's the encrypted backup on the USB drive that I wanted to use. From that point on, everything has worked well.

I have no idea if the problem is the way M.A. handles encrypted backups or if there was some other issue. But hopefully if anyone else runs into this problem, clicking on Continue will take you where everything finally works.