IF you balance the tiller in just the right position, with the right amount of tension.
Use two 24 inch bungee cords, or maybe less if your cockpit is narrow, and two pieces of 10 gauge solid strand insulated copper wire, like they use in a house for the water heater. Tie the ends of the wire to the post of the stern pulpit abeam of the forward end of the tiller. Afix the ends of the bungee cords to the end of the tiller, and make loops in the wires for the other end of the bungee so the tiller will be near the center. I made several loops so I could adjust the tension on the bungees and the position of the tiller by putting the ends in a different loop. Thus the tiller would be held in the proper position, BUT WITH SOME GIVE in both directions. I just bent the bungee ends to fit in the hole in the tiller for the tiller extension. To disconnect I just pulled the bungees out of the tiller.
To set the sails, get on the course you want and set the sails properly, so they are both producing maximum power. Then overtighten the jib somewhat, you have to experiment to get it right, but you want it stalled a little. If you have tell tales, the ones on the front of the sail will stop their staight backwards position and do funny things. Also loosen the mainsheet just a tad, so you have some luff. Yes, set the jib too tight and the main too loose.
Now try to tie the tiller with the bungees to maintain this course, and instead of "course" think "point of sail". From a beam to close reach is the only place I could make it work reliably.
What happens:
Sailing along, you have the normal weather helm pulling the tiller to leeward, but you set the bungees to maintain the course, so the tiller is slightly to windward. The jib is slightly stalled and the main is luffing a little.
1. Wind shifts to beam:
If the wind shifts slightly to beam (a lift), the main, which was a little loose, is now set for more power! the boat heels more, causing more weather helm. The jib is still stalled, which also makes the boat want to turn upwind. This we usually notice as an increase on tiller pressure as the boat heels over. The windward bungee stretches from this increased pressure and the tiller goes to leeward, adding to the heeling hull's desire to head up. The boat turns to windward. As she heads up, the main starts luffing again, as she heels less the rudder comes back to windward by the bungees. If she turns upwind just a little more, the previously stalled jib comes into the position for max power and helps stop the windward turn. As the jib pulls the bow down wind, it stalls again as the main starts filling. If you have "balanced" the boat, it will oscillate back to a steady course.
2. Wind shifts ahead (a header):
As the wind shifts ahead, the main luffs even more and the jib goes from stalled to max power, pulling the bow downwind (bears off). Also, as the main loses power the boat heels less and two things happen. The tiller moves slightly more to windward and more of the windward hull is in the water, both help the jib bear off. As it bears off, the jib stalls again and the main comes back up to power, stopping the turn.
It's really quite fun to try, but remember if the windspeed changes your tiller and sail settings will be wrong! You can have it set perfectly balanced, and just a move to the other side of the boat and it won't be just right anymore. This is a way to give your arm a rest, not a way to leave the cockpit for extended periods.
Tying the tiller with two bungees makes it work infinitely better than just lashing it down, because it allows the boat to move the tiller by itself. This method will sometimes work with the tiller tied firmly in position, but not nearly as well.
Once you have the boat balanced well, you can proceed to steer with the sails. By easing the mainsheet the boat will turn downwind a few degrees. Loosen the jib a tad too to keep the boat balanced. Tying the tiller a bit more to windward will also change course downwind.
To change course upwind, tighten the mainsail and perhaps reposition the tiller a tad toward leeward.