Figured I'd share an interesting story about something I wasn't aware could happen.

It all started when I tried to wire a trailer tail light that grounds through the frame. I bolted it up, wired the ground, and started poking around to try and figure out which was the running wire and which was the brake wire. Well a bit of carelessness on my part, one of the live wires brushed the now grounded base of the light without me realizing it and a fuse blew. The light went dead, but because the engine wasn't running it had been dimming a bit the whole time. I thought that I had just ran the battery dry. I am no stranger to dead batteries so I went about trying to bump start it.

It was rough, but after removing the tail light and 30 minutes of pushing it up and grinding down a hill it finally started! The engine would fire about every other rotation, and if I turned the throttle it didn't have enough juice to fire any faster, it would still only fire about once a second, so it only fired 1 in 3-4 times. This got me curious so I turned on a blinker and it almost died. Then I turned on the high beam and it died.

15 more minutes with that god blessed hill and it started again. Same condition. I still thought it was the battery so I let it run for awhile, but it didn't improve. I figured the best way to get the battery charged was to increase the engine speed, but I couldn't do that just sitting in neutral, so off I went riding this zombie of a bike. I found that if I could get it rolling by slightly twisting the throttle I could  keep it going just idling. I could then get it to 2nd and reach 20-25mph under idle power. I could even get surges of power if I engined braked and then twisted the throttle!

This went on for an hour or so and then I gave up and decided to check the electrical system. After going over the wiring diagram for awhile I realized that all of the dead systems were routed through a single fuse. I checked the fuse box and found the blown fuse. Replaced that and it started right up.

Lessons learned: If this fuse is blown the lights will be off with the key on, and the starter will not turn over. However, the bike can be bump started and it will idle, if just barely. Once it is running it will appear normal except for slightly flickering lights and being unable to run faster than idle.

Bike info: 2004 with stock wiring except for a stripped taillight.

Could be useful if you are stranded with a blown fuse and need to get somewhere.

I wouldn't relie on it even for limping home as it maybe just your bike that'll do it..
Either a ground loop or a short or maybe just a weak spot in the insullation of a wire.
What tells me this is the weak spark.  As 360 noted, the battery acts as a buffer.  The fact that it's only sparking 1 in 4 times probably in sync with the lights pulsing.  I know when I had a loose plug and the battery wasn't charging, the final straw was to turn the blinkers on and it would miss with every blink.