Which single pilot aircraft had a range of at least 2160nm in the late 90s?
Smaller planes that had this range back in the 90's were not so rare, but they were jets, most of them were not intended to be operated, at least commercially by a single crewmember. It would have been totally possible though.
When considering that you are writing a book, you may take some liberties (in addition to the crew count) when it comes to range: the official figures take into account the fuel reserve regulations, so after the declared range is flown, the plane would most likely be able to continue flight for about an hour before fuel starvation.
So, at least these had the range of 2160nm minimum (some not fully loaded):

Learjet 60
IAI Westwind
Dassault Falcon 20 (some variants)
Hawker 800

(To keep things simple, I'll turn this into community wiki right away)