The reason I like using a bungee is that you can immediately and easily override it physically (without having to untie or unhook it) if you start to get tacked by a big wind shift or a powerboat wake, or have to take evasive action to avoid another boat, etc. (Maybe I'm just a control freak. )

I had fun experimenting with my system. The version I like best is using one piece of bungie, the center of which is tied at the center of the aft beam. And each end of that bungie has a hook on it. (Just a regular, open hook.) When not in use, the hooks are hooked onto the aft lacing of my tramp, one at each side. Since I have one hook on each side of the boat, if I need to park on starboard, for instance, I just grab the hook on the starboard side and put the bungee around the starboard tiller arm at the joint with the crossbar, and hook it to itself. The only thing you have to figure out is the length of the bungee. If it's a little too long or you need more pressure to hold the tiller over, you can just wrap it around more times. And for most cats you don't need a very heavy-duty bungee. I don't have a tiller extension on my current boat, but I would use my method even if I did have one.

Try some things and let us know what works best for you.