The brake light & battery light on my 2001 Q45t are lit. There doesn’t seem to be any connection between these, plus the battery is new.

Have the charging system checked. When both of these lights are on it normally means the alternator isn’t charging properly.

When you refer to “the brake light”, I am assuming that you are referring to the warning light for the brake system, not the brake lights on the back of the vehicle. With that assumption, I can tell you that if the brake warning light and the “battery” light are both illuminated, it usually means that your alternator is on its way out.

And, this can frequently result in the battery failing also, due to the alternator putting out an insufficient charge to the battery. You would be wise to have the alternator checked a.s.a.p., before you wind up being stranded somewhere if and when it conks out.