I agree co-pilot would log p2 when in seat…but normally the total time of flight should count towards flight time limits. Under the FAA you are limited to 1000 hours total…not just 1000 hours of P1 or P2.
I would think if you do a 12 hour flight you should log 12 hours total time….p2 may only be 4.5
and talking about duty times I believe they are up to 23 hours….but that is a different story