comma with 'that' [relative pronoun]: the watch, that is on the...,

The watch(,) that is on the table(,) belongs to my brother.

Are the commas needed? I don't think so.

Am I correct?

Thanks.

I don't think it should have commas.

Thanks, Egmont.

I agree, they're not only unnecessary, they're wrong.

The watch, a genuine Rolex, belongs to my brother. (Here, "a genuine Rolex" is another way of saying "the watch," so you need the commas.)

The watch which is on the table belongs to my brother. (Here, you're describing which watch; not the watch on my wrist, not the one in the drawer, the one on the table. No commas, because they are further specifiying the watch.)

See the discussion here of nonrestrictive and restrictive appositives.

It depends on what you want to say. Is there some reason you didn't just say "The watch on the table belongs to my brother"?