That is for a Cunningham. The Cunningham applies tension to the mainsail luff drawing the belly of the sail forward. It is typically a block and tackle secured at the base of the mast and with a hook that goes into the Cunningham hole.
The main halyard also tensions the mainsail luff, however, it also tensions the leach. The Cunningham counters some of the leech tension because the pull is only vertical. The halyard tensions in 2 directions, along the luff and leech
It is a flattening reef. Sometimes you only want to take out some of the sail's fullness, the flattening reef does that, it pulls the shelf into the boom and reduces draft along the lower part of the sail.
The last time I saw one of those was on an Olson 40 - thirty years ago. It was very effective. It could make that main flat as a piece of plywood. I don't think the flattening reef lived past Dacron sails but that is conjecture. You could contort Dacron sails into various shapes. Laminate sails are largely the shape they are.
As for the question on how to use them: I think you'd want tension on both the luff and tack. One loose and one tight would seem to me to stress the sail.
I had a C25 with a flattening reef and used them independant of each other. The tack was used for the Cunningham to tension the luff and the clew was used to pull the belly and draft out of the foot just above the foot shelf.
Thanks for asking this and for all the responses. I have a "new to me" Cal 27-3 and was just web searching for the same question. This also explains why there is a assembly of blocks and line I found stored inside. Must be the Cunningham.
The manual says there is an internal outhaul and reefing line within the boom. So I'm guessing that this reefing line is used to flatten the sail as mentioned above and not to reduce sail area in the "usual" method of reefing the sail.