ILS critical area when the tower is closed?

In this month's AOPA Flight Training magazine, I read an article
which implied there was still some requirement to remain clear of
the ILS critical area even when the tower was closed.

I've been looking through the AIM, and can't find anything like
this. It does say that when the tower is open, it will keep the
area clear when there is an aircraft past the FAF and the weather
is below 800/2.

Is there a rule which states that the ILS critical area must be
kept clear at any time when the tower is not in operation?

Can you please provide a reference?

Thanks,

--
Mark Hansen, PP-ASEL, Instrument Airplane
Sacramento, CA