Elon is only permitted to work for 130 days because he's an SGE. The last day is May 30, which is 130 days after Jan 20.
A "special Government employee" (or "SGE") is an officer or employee in the Executive Branch of the Federal Government who is appointed to perform important, but limited, services to the Government, with or without compensation, for a period not to exceed 130 days during any period of 365 consecutive days.
A "special Government employee" (or "SGE") is an officer or employee in the Executive Branch of the Federal Government who is appointed to perform important, but limited, services to the Government, with or without compensation, for a period not to exceed 130 days during any period of 365 consecutive days.
https://www.doi.gov/ethics/special-government-employees