I cook them together and separate the point after I’ve pulled the whole thing off the smoker and it’s been resting for at least an hour(*). I let the flat continue to rest while I chop, season, and sauce the burnt ends before returning them to the smoker for another hour.
(*) I only deviate from this if the IT of the point is NOT lagging behind that of the middle of the flat. Usually this isn’t a problem because the point is much thicker than the middle of the flat, so when the middle of the flat is at 200-203 the point should be closer to 190. If the point gets to 200, sometimes I have a problem with it falling apart as I try to chop it. So when necessary I will separate and pull the point off while the flat continues to cook, but you lose some valuable juices in the process.