Leash on the surf board goes to the skeg or a small cup with a pin across that is glass into the board around the skeg. Shockcord leash attaches to your ankle.
For the kayak,,,,I leash my paddle to the side of the boat with a short 3 foot coil leash on the port side.
I leash the boat to my wrist with a velcro wrap that has a pull tab. The shockcord goes to the rear of the kayak down the starboard side. I coil wrap and tuck it under deck rigging, a small bag could work also but I have never found the need. So there is no extra length of cord flopping around. When I end up in the water if I can't hold onto the boat the shockcord simply pulls away. I pull the boat to me or swim a short distance just like I do when surfing. I do this on a sit inside sea kayak and sit on top fishing kayaks. I keep my decks clean and free of any obstructions/snags as much as possible. That is not always feasible on a sit on top for offshore fishing. It is however more easily accomplished on a sea kayak.
Just another point in this discussion which I forgot to initially bring up. Different from a kayak tether which you end up in the water but sort of relevant.... Sailing.....you use a safety harness and short lifeline that attaches yourself to the sailboat. Rough seas come up you clip on. This is often done whether you are sailing solo or crewing a boat. When crewing in rough seas and you go up on the foredeck to deal with a jib/sail for instance or to perform what ever function....You clip into a safety harness/lifeline. A gust comes up and swings that boom around and knocks you over the side or you slip off a wet deck...you are attached to the sailboat with a short safety line and harness and prevented from ending up in the water. A sailboat can end up upside down rolling several times. There are all sorts of lines/rigging/running rigging, winches, cleats, the mast and the boom etc. YOU STILL USE a lifeline to attach yourself to the sailboat. Food for thought..........
Curious where does a leash go on a surf board?
When you leash yourself to a kayak where do you put it on you body?