A Special Government Employee (SGE) can work no more than 130 days during any consecutive 365-day period.
They’re allowed to maintain private-sector jobs or other roles.
They are subject to federal ethics rules, but with some exceptions or leniencies given the part-time nature of their service.
They can be paid.
Elon Musk is a SGE.
He won’t be paid though.
https://www.law.cornell.edu/uscode/text/18/202