The age of last commit on trunk is a useless metric in isolation. The fact that it is the most prominent number on the front page of a repository is a shame.
A metric I think is useful is responsiveness to issues. If there haven't been any recent commits and if I open the issue tracker and the maintainer hasn't even acknowledged issues that have been opened in the last 6 months, then I assume the project is no longer maintained.
I would love to see a metric of the number (or proportion) of issues closed even though users are trying to get assistance. No idea how to make that machine-calculable though.
Even better, a metric for refused PRs (maybe including PR size somehow), tracking where users cared enough to try to contribute and the owner just refused to accept the changes. Easily gamed though.