Tume,
It's my understanding that you cannot log anything unless you are a "required crew member" or are "the sole manipulator of the controls."
According to Wiki, the PC-12 "is certified for single-pilot
IFR operations, though operators may choose to use a second flight crew member."
It's what the type certificate says that makes someone second in command, not an ops manual. You can log the time in the PC-12 as PIC if you are "the sole manipulator" but there's no SIC time. If you are logging PIC in the right seat (sole manipulator) the the person is the left seat isn't.
Many Citations are single-pilot aircraft, even if operated by two. If the CE-560's type certificate requires two pilots, then your time will be logable.
Go to
www.askacfi.com and search on logging flight time. You'll find pretty much every permutation under the sun there!
Terry