Kickdown Question

But it should hold it for more than 3-5 seconds, right?

As bad as the P.O. had the linkage messed up, I'd really like to check the lower adjustment as well.
As RPM's build up, the pressure also builds. When the pressure reaches the max the governor allows, it will automatically upshift to 3rd. This assumes, obviously, that you leave the gear selector in "D". If you manually put the gear selector in "2", the trans will shift from first to second and should stay in second until you manually upshift to "D".