I would assume his commanding officer.
What is their recourse if he continues to refuse?
Court martial for violation of several of the punitive articles of the UCMJ. Followed by dismissal from the service if convicted, loss of pension, possibly time in Leavenworth.
...What is their recourse if he continues to refuse?
Discovery of what? He's going to be charged with disobeying orders of his commanding officer or some other officer in the chain-of-command, missing movement, and probably some other UCMJ violations as well. What's going to be uncovered in that?
Which ends eventually with the CIC. Then discovery could be used to ascertain if the CIC is eligible.