He asks: Is it permissible for a non-Muslim to enter the mosque to wait?

By Allah, regarding this issue, it appears—and Allah knows best—that it is permissible for a non-Muslim to enter the mosque.

The one who is not allowed to enter is the Sacred Mosque, as Allah the Blessed and Exalted said: The polytheists are impure, so let them not approach the Sacred Mosque after this year.

As for other than the Sacred Mosque, it appears—and Allah knows best—that it is permissible.

And the Prophet ﷺ, near the end of his life, when he captured Thumama ibn Uthal.

And Thumama ibn Uthal, meaning.

He was a disbeliever, before he became Muslim, of course.

So he tied him up, or ordered him to be tied, to a pillar in the mosque.

Like the one tied in the mosque, and the delegations in the ninth year.

They would come to the Prophet ﷺ, disbelievers, most of them were disbelievers, they would come and speak to the Prophet in the mosque.

They would meet him in the mosque, so it appears—may Allah curse—yes, it is allowed.

For a disbeliever to enter the mosque, except for the Sacred Mosque.