You said that only some of your commute requires the 20w headlight. Run the light off a 6v SLA battery. Then run the white wire through a single diode to keep the battery trickle charged. Because of your large headlight, you will only be able to run it about 10 or 15% of the time without depleting the battery. Choose the battery accordingly. Each amp-hour will give you about 15 minutes of continuous headlight run time. Besides acting as a rectifier, the diode will prevent the connection from killing the spark output.
I use a complete setup (brake light, headlight, tail light, turn signals, horn) that includes a much smaller headlight that I use occasionally. The 1.3ah sla battery has stayed charged after 7 months and 1000 miles.