When coming from Furnace Creek (rte 190), one goes 6 miles S on the Badwater Road, then turns SW on the Westside Rd. Take the Westside Road 11 miles to the Shorty's Well / Hanaupah Canyon crossroad. About 1.2 miles before reaching the Well Rd, there is a sign for "Tule Spring".
It's good to plan this hike for a waning moon that rises at midnight-1 AM, so the moon will be up and bright when you start out at 3-4AM (for Oct-Nov). Headlamps are a good extra, but if the moon is bright, there is a good chance you won't need lamps on the road, and the sun will be up before the road ends.
There is a detailed description of this route in the guidebook "Hiking the High Sierra" by Branch Whitney.