Hi Ken,
This is a tricky question to answer without more visibility over your site, the video and the overall plans - but concretely I'd probably just recommend getting the video indexed on the main page you want to rank with that video. Having the same thumbnail appear across a number of pages can be a bit weird, and is ostensibly the same as having duplicate text across multiple pages - that is to say it can cannibalise rankings if done at scale.
Thanks,
Phil.