Nighttime paddling is very cool. Get out and try it!
more specifics on the regs:
After some research, the 360 rule I saw was taken from Texas regs (maybe other states, too). Washington has no specific laws beyond USCG's.
"All vessels including motorboats, sailboats, canoes, kayaks, punts, rowboats, rubber rafts, or other vessels when not at dock must have and exhibit at least one bright light, lantern or flashlight visible all around the horizon from sunset to sunrise in all weather and during restricted visibility. "
National USCG regulations:
"Vessels under oars may display the lights prescribed for sailing vessels, but if not, must have ready at hand an electric torch or lighted lantern showing a white light to be displayed in sufficient time to prevent collision"
"sufficient time" : One thing to consider if you're paddling around boat traffic at night is that they can come up on you from behind pretty quickly (esp. if they don't see you). I started putting my light on the back for this reason (btw/ it is annoying to look at on the bow). Unless you're constantly looking back or trusting boaters to be vigilant, I wouldn't count on having sufficient time to turn on your light.
One way or another, do what's safe and have fun.