Listen to the "Night Carrier Landings" episode of The Fighter Pilot podcast. They essentially end all of the speculation in this thread.
If I'm understanding them correctly the CASE III holding pattern can occur on any radial from the carrier, but is typically somewhere behind the ship. It's the marshall point that has to be on a 180 radial from the ship.
Pilots are assigned a designated TOT of sorts at the Marshall point, and are expected to hit that marshall point very closely. The podcast made it sound as if they typically hit this down to the second, or very close to that.
Pilots do orbits in the holding pattern and use standard rate turns, half standard rate turns, and quarter standard rate turns and do math in the cockpit that enables them to be on the correct bearing and speed at the exact right time so that they arrive at the marshall point as directed.
Don't skewer me if the manual says this is incorrect, I'm just telling you what two Navy pilots with actual night trap experience said on one podcast.