Dottie and I have never been asked to leave a rest stop, and we've
stayed in dozens of them all over North America.  We usually pop up
the top also.

We interpret signs that say "no camping" as meaning "no setting up a tent."

We interpret signs that say "no parking for more than x hours" as
parking your vehicle for x hours and leaving it unattended.  If you
are in the vehicle, you are not parking, you are stopping.

Of course, YMMV.

couple of suggestions;
1) carry earplugs, you may be close to idling trucks all night
2) keep your cellphone close, in case of emergency

>1. Pull in.
>(1.a  Check for large signs saying "no overnight parking ever under any
>circmstances, no sleeping, no spending more than two hours here."  Some rest
>stops have signs that say "no camping, no staying here for more than ten
>hours at a stretch unless it's an emergency which includes blizzards or you
>are too tired to keep driving."  That's an invitation to overnight, if you
>ask me.)