The first stereotype is the notion that J's are always on time, and P's are always late. IT'S NOT TRUE!
Two J's live together in my household, and we're often late for appointments. In fact, the standing joke around here is that "J" stands for "Just One More Thing!" -- meaning we invariably try to accomplish one additional thing before we charge out the door. We do not have a reputation for reliably being on time (ask my sister!).
In contrast, I've met P's who arrive at the airport several hours ahead of their flights, and arrive well in advance of any meetings. (Interestingly, one P admitted to me that he arrived early as a way of compensation for an acknowledged tendency to be late. Viva le compensation!)
The point is, if you're using a stopwatch to distinguish P and J, you are wasting your time.
Another myth is about Js being tidy and Ps being messy. Whoa again!
The messiest house I've ever seen in my life belonged to an ESFJ. It looked like a garage sale gone mad -- with a layer of dust everywhere to boot! The "J" house I live in with my husband looks like a tornado went through it last week.
Do you know who's probably the tidiest person I know? My ISTP dad, of course. (Notice the last letter, willya?) I also spent 8 years living with an ENFP -- and he would win the neatness award long before I would even be eligible. So saying J's are tidy and P's are messy is FALSE!
Then there's the added problem of people who try to figure out whether they are J or P based on these same criteria! Well, as the Mafiosos say, "fuhgettabouttit!"
Linda Berens has said that NJ often looks like P. And boy is that ever true in my NJ household. What's interesting is that my husband and I score equally on any questions of early-starting and pressure-prompted -- because we do both! Since the two of us possess the Chart-the-Course interaction style, we tend to put just enough energy into an event early on in the process to figure out what must be done to arrive at the goal point. But then we forget about the whole matter until we're "pressure-prompted" to actually set the wheels in motion for the event. Invariably, we cut the margin too finely, and quality of life can be rather questionable until the event has ended.