Other than SDO it'll be the first watch you're "qualified" for (here's the book, record the interval, don't suck - training complete) so it just rotates among the JO's who are not LSO's or standing SDO.
A corresponding watchbill is stood in Air Ops by LCDRs for Case III recoveries although they get to share seats with XO/ COs and even DCAG/CAG who drop in to watch so you may get called out b6 Air Ops or DCAG/CAG.