I am having intermittent battery light problems, too. My truck is an '06 4.6 with about 24k on the clock. My symptoms don't match the OP's, but my dash battery warning light is on quite a bit now. I notice it's on more than it's off, but the type of driving doesn't matter, nor does the position of my pedals (gas on, gas off, idle, high revs, etc.).
I first noticed the light last Sunday (a week ago today) after driving through E. Ohio in some of the worst rain I have experienced in a long, long time. It was pouring.
After seeing the light, I immediately set one of my readouts on the Edge Attitude to display the 'Batt Charge' reading, and it never displays a read out under 14.2 or 14.4.
Is the idiot light indicative of 'throwing a code'? Can my Edge read that code?