The requirement for holding a first class medical is in the FAA FSIMS, the updated version of the inspectors handbook.
ELIGIBILITY FOR THE ATP WRITTEN (KNOWLEDGE) TEST. Test examiners administer aeronautical knowledge tests in written form or by computer. Since these tests can be administered by both means, they will be referred to as knowledge tests. Before an applicant may take the airline transport pilot (ATP) knowledge examination, however, an inspector must establish that the applicant is eligible for the requested certification in either the airplane or rotorcraft category. Except for age, applicants must meet all eligibility requirements before being authorized to the ATP knowledge test or being issued a Federal Aviation Administration (FAA) Form 8060-7, Airman’s Authorization for Written Test. Inspectors should use either the job aid entitled, “ATP-Knowledge Qualifications Job Aid-Airplane” or “ATP-Knowledge Qualifications Job Aid-Helicopter,” as applicable, to complete this task (see Figures 5-110 and 5-109). The eligibility requirements for the ATP certificate are printed in an abbreviated form on the job aid. The following is an expanded discussion of the eligibility requirements.
A. An applicant must submit documentary evidence to show at least one of the following acceptable pilot qualifications:
·An FAA commercial pilot certificate,
·A commercial or ATP certificate (without limitation) issued by an International Civil Aviation Organization (ICAO) country, or
·Evidence of United States (U.S.) military pilot qualification within the past 12 calendar-months (such as aeronautical orders or flight time logs).
B. An applicant must process a current first class medical certificate.
C. An applicant must be a high school graduate or the equivalent. ...
D. An applicant must be able to read, write, and understand the English language. ...
E. An applicant must be of good moral character. ...
F. An applicant must have accumulated the flight experience required for the appropriate category rating before taking the knowledge examination. Each applicant must submit logbooks or other equivalent documents for an inspector to verify the flight experience. ...
Since Silver Knapper is getting a business jet type, he won't be "exercising the privileges" of an ATP and so will only need a second class medical.