The former race car driver-turned-broadcaster was in the middle of his coverage of Sunday's Grand Prix down in Miami for Sky Sports ... where he was flagging people down for interviews on the speedway grid like he usually does each year.

Unfortunately, he manifested a case of mistaken identity ... doing a stop-and-chat with the star Duke basketball player -- who towered over everyone at an impressive 6'10" -- whom he apparently thought was the Kansas City Chiefs star QB. It was funny ... and kinda cringe.

Check it out -- you see Brundle spot who he thinks is PM, and shouts out his name ... only to be ignored by Paolo. When he finally catches up to him though ... he gets his interview.

After a few seconds, MB realizes Paolo isn't Pat ... and sorta apologizes as Paolo goes on his way. Doesn't seem he was sweating the mix-up either, dropping a "whatever" afterward.

At one point, Brundle came across a rando that he seems to have thought might've been famous -- but rather than make the leap he did with Paolo/Patrick, he politely asked ... who the heck are ya??? This interview didn't go so great either, though ... but made for good TV.