6 months ago, my bluey did exactly what you have described.
As you have already suggested, the first thing to do is pull the dizzy cap off, take off the rotor button and then remove the black plastic cap that covers the cam position sensor. Chances are, it will be full of oil.
If this is the case, buy a can of contact cleaner and give it all a good clean out. I drilled a couple of small drain holes in the bottom of my cam pos sensor cover, so that any oil that makes it in there can drain out overnight. Haven't had a problem since.....
Let us know how you go...
Dan.