I have a single set of reef points and have
- One eye on the rear Starboard side of the boom
- One reef cringle in the leech of the sail
- One cheek block on the rear Port side of the boom
- One cheek block at the front Port side of the boom
- One reef cringle in the luff of the sail
- One cheek block at the front Starboard side of the boom
- One cam cleat a bit aft of the cheek block at the front Starboard side of the boom
My single reef line connects all of these (in order from fixed to working end).
Now for reefing you want to pull the rear of the sail back and down. The eye and cheek block in my setup are not opposite of each other, so that one part of the line pulls down and the other pulls back. There may be some fitting near the end of the boom on the side that we can't see? Normally, by having the line go
through the reef cringle, you pick up a 2:1 purchase. (And you have a line on both sides of the sail, holding the reefed portion in place.) Conceivably, you could also
tie the reef line to the cringle, saving the eye.
At the front of the boom, you could have a setup where the reef line gets led down the mast. (And where the luff of the sail is held by a reef hook or by some line tied through that cringle and also led down the mast, or simply wrapped around the boom.)
If the previous owner used the front cheek block to lead the line down (instead of up into the sail) then there should be cleats somewhere on the mast for it (unless they re-used the cleat for the gooseneck downhaul). Or they could have lead the line up, but on the return, not used a cleat on the boom, but one on the mast or deck.