Indeed, a bad relay.
To complete this thread - the brake lights relay went bad. In 2002 models this is actually a recall item, but 2001, which has the same relay is not a part of this recall.

The relay is question is a double size relay, and the solution is to replace it with two separate relays. To make things more confusing Volvo recommends two different part numbers for the two replacement relays. So when you buy these replacements they sell you two different relays. They are identical in shape and fully interchangeable, but part numbers are different.

The dealer was not able to tell which relay goes into which socket. They just install them randomly. And this is what I did. Everything works fine.

I suspect these two relays are identical inside, but made by different suppliers.

Hope this will help