Annex 1 states that the crew must be qualified to fly the aircraft with a type rating. Generally, you can happily fly your C680 in the USA and no one will ask you to prove that you are qualified to fly that aircraft. In Europe and in compliance with ICAO, they will ask you to prove it. So make sure you comply with FAR 61.55.....
This is from the US NBAA..
Second-In-Command Type Rating
Updated February 22, 2007
On August 4, 2005, the FAA released a final rule on the new second-in-command (SIC) pilot type rating to bring the U.S. Federal Aviation Regulations into compliance with international standards on pilot certificates. On September 9, 2005, the FAA reissued the final rule to correct the compliance date.
Second-In-Command Type Rating | NBAA - National Business Aviation Association