Brief report:
Started at 8:36am from the Vivian Creek trailhead. Didn't take much water and so went a slower pace than usual. Left the main trail around 10,200' (this is 10-15 minutes after reaching the 10,000-foot ridge saddle where you see first see the Dragon's Head). Dropped down 200 feet to the small creek below and went up the West Slope of Dragon's Head. Reached the summit at 12:56pm. Had lunch and then headed to San Gorgonio's summit via the south slope. Descended via the main Vivian Creek trail down to the car. A nice day out in the local mountains.
Additional info about climbing Dragon's Head can be found here.