At the risk of getting into an "argument"...……
It's important to point out that Nichols and several other Interpretation Letters on this particular subject are based on the Citation 525 Series of aircraft and NOT the 500 Series. The difference is that the 525 are Type Certificated as Single-Pilot Aircraft and the 500 Series are "two pilots required". In a 525, no exemption letter is required to fly single pilot.
In Nichols, the Certification of the PILOT was an integral part of the question presented to the FFA (yeah, I know). In a 525, I can hold a 525 Type Rating and an SIC is required. IF (big IF), I hold a 525
S type rating, I do NOT "require" an SIC.....UNLESS the autopilot is inop. If I hold a 525S type Rating, then, as
@MidlifeFlyer mentioned, I can't "unqualify" myself just so the pilot next to me can log time, this isn't an option. I can't unqualify myself because the training, and the "S" in this discussion, are part of my type rating and qualification to operate the airplane.
A pilot can not achieve a 500
S type rating as it does not exist. In a 500 series, the only way to fly single pilot is with an exemption letter. A pilot holding an exemption has the option to NOT exercise the authority of the exemption by simply NOT having the Letter in their possession during the flight.