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No. You need two. You need power and grounds for the "high" part of the bulb. If you look closely, there are no contacts other than the ones for the running lamps for the top bulbs. It's easiest if you run wires from the bottom bulb contacts to "make" contacts for the "high" part of the top bulb.
I am so lost now I just want to call it quits. I got the same result using one wire from the middle bulb to the top bulb. So whats the need for 2 wires?