If you plan to add a rub to a brisket, when is the best time to do this?

You can put the rub on the night before or just before placing in smoker, or not use any rub at all if you want. I tend to put it on just before(maybe an hour) smoking. I don't see a big difference if it stays on overnight.

Due to hurricane Jeanne, The last brisket I smoked I put the rub on 24 hours before smoking and the salt in the rub seemed to pull the juice out of the meat. It was very dry when done, the only time this has happened. Barring any hurricane sneak attacks in the future I won't let the rub stay on longer than overnight.

Many brisket cooks try to get it on at least a few hours before going on the pit.

They often add another heavy coat of rub to the brisket,while the pit is coming to temp.

That is the approach we take.

I, personally, don't worry about the rub drawing appreciable moisture out of our briskets.