Several different ways of doing this-all fairly simple. For the leash itself you can use a coiled cell phone cord as I posted about some time ago. However, that means the cell phone cord is stretched across the cockpit and gets in the way of my foot.
A better way is to use a length of parachute cord or a nylon strap, or similar cord of some sort to which you can add a carabiner or a snap hook.
In my Outback, I have used a nylon strap that came with a camera. One end is attached to a cleat or an eyestrap, and the tag end is attached to a snap hook that goes in the drive adjustment hole directly.
Here is the same setup in my wife's Sport showing the whole leash.
Closer view of the leash where it attaches to the drive by means of a snap hook:
More recently, I have gone with a new solution to make it a bit easier and faster to hook and unhook the drive unit from the leash itself. Just add a SS shackle to the last adjustment hole on the Mirage Drive itself. Then it is a simple matter to hook and unhook the leash by means of a SS carabiner. The reason for the change was that I was not quite certain the snap hook would stay firmly attached in the event of a flip and all the scrambling around in and under the cockpit. However, I have little doubt that the carabiner and shackle would remain securely attached if the boat was upside down, and the drive unit was dangling down in the water.
BTW, for the attachment of any type of paracord leash to a drive or any other equipment (knife, pliers, lip gripper, etc.), your best bet is to use the bowline knot. It is easy to tie, and especially untie, since it won't jam like many other knots. It is also very secure, especially if you add a couple of half hitches to the tag end. For 99% of all lines, it works great--the only exception being the very stiff yellow synthetic lines that you sometimes see being used as dock or anchor lines. These lines are so stiff that the bowline does not lay like I would prefer. It still works, but you have to eyeball it from time to time to make certain it is secure.