The 565 quick sets by pumping the crown from position 2 (time set) to position 3. Your watch probably has a 562 - the same as the 166010
I sold here. It (semi) quick sets by cycling between 9pm and midnight as the seller says. There is a link in my sales listing to the service document I made for that watch and you can compare the movements. Your one is desperately in need of a service but, it might come up okay. I think those are jewels that your seeing next to the "24 jewels" writing - they are just very, very dirty.
If the BOR is in good condition, $600 doesn't seem too unreasonable (a bit high but the BOR could be worth $150 on its own) although, expect to add at least half that for a service/parts. Depends on the dial really as if it is spotted badly then I'd steer clear. The problem is these sort of watches with dirty/neglected movements can be real money pits so, you're taking a big chance...
Cheers, Chris