2001 Ford Ranger Battery light

About a week and a half ago my battry light came on and the gauge needle dropped to just above the bottom peg. Seeing as it was the original battery, I went and got a new one. Put it in, all looked good. Drove the truck less than 5 miles and the battery light came on again, needle dropped. Went to Schucks and had the battery and alternator tested. Battery was at full charge, cranked well, alternator tested good. The belt showed no vibration, cracks or sounds. So we thought it might be a sensor or a wire. I DO have squirrels around here and find peanut shells from time to time on top of the engine. Maybe one nibbled a wire. But I have looked and not found anything.
Yesterday I ran an errand. Truck made one brief hiccup when I went to turn it over but then it cranked just fine and turned over. Drove about 10 miles. When I went to get in the truck, I got nothing but a bbrrrrr sound. I thought selenoid, but most selenoids make a tap tap tap sound. This was faster. Had a buddy come meet me. We tested the battery 11.3 volts. Should at least crank, shouldn't it? So we thought maybe the starter. Pulled the starter and took it for bench test. Tested good. Selenoid tested good. Went back and put starter back in. Battery now tested at 9.5. Checked all of the grounds. Only one we couldn't get to is underneath back up against the firewall. Even tried popping the clutch to start. It did turn over, barely, but I had to keep gunning the gas to keep it going. Finally, last ditch, we tried jump start from his battery. Turned right over. Followed me home. Half way, the battery light comes on. Get home, checked the battery. 12 volts.
Tried a restart, no problem. We are stumped. Please help! And what does the ignition coil do? Could it be that? We could find it. Thanks guys.