I found one by the United Nations. In the meanwhile Paul starved to death.

"Youtube Time Filter" Chrome extension

by searching for the length in your favourite search engine :)

There doesn't seem to be a way to search YT videos (except videos you yourself post) by exact length. I got 21 min 45 seconds. Looking up "3000 second timer" on YT got me close (only 4 seconds out), but not exact. Do you have a way to find exact-length videos that I'm missing?

I found exactly the video I needed by searching "38 minute video" and one of the "timers" was the required 37m58s, but Paul died just as I found it.

It would have likely screwed up your previous answers -- roman numerals etc.

I think you just have to search for it and hope for the best, my query got me this video which is hilarious: https://www.youtube.com/watch?v=RRoUEr1l0n8

I figured out a way to get a list of videos all matching the time you want. Should help. https://news.ycombinator.com/item?id=36499194