since it's the winter time, i say it's the corrosion around the terminal of the battery. clean the terminal and just to be sure, go to any auto stores and have your battery checked. they should give you a free testing on batteries.
this is what i would do.
run the power wire to a relay. the trigger wire will go to the switch. and that's for your first switch. you won't need a fuse.
for the LED, run ANOTHER wire from the battery to the fuse, then to the switch. the output of the switch goes to the LED. everything should...
So some of you may already know about the situation i had with m '99 Honda Accord. Long story short, 7+ accidents (not by me). BUT ANYWAYS! I know drive a '09 Honda CRV and i am loving it! I'm somehow still active in this forum so just wanted to share some pictures i took today. Enjoy!