Aside from all the stuff in Dale's trunk, I carry a parts cleaner, complete welding supplies, portable paint booth... -just kidding. I do carry a few tools in the trunk, but my TR6 has only let me down on the road ONCE in more than 20k miles and 4 years. I don't like rattles and don't know the 'correct' method (probably using that leather strap under the tire somehow), but here's how my jack, tool and handle stay quiet.
If you look closely at the picture of the jack, you'll see the cell phone charger I'd been looking for, and under that is the jack handle. You can't see the tire tool, but it's under there, held in place by that big wing nut.