Brilliant moves are rare, but out of the 87 games I played I have 8 brilliant moves! Interesting that some players rated much higher and have more games played may have only a single brilliant move. Perhaps because I play Daily chess where I have time to analyse and look for tricky moves.
For the same move in the same position, they are awarded to weaker players but not to stronger ones. Also there's a higher chance of getting one if you already made a bad mistake a few moves before.
I've never had one!