3.0 Ltr Auto Electrical Problems

Hi All,
I have a 2002 ZD3.0 auto Patrol and when I first start up in the morning several dash light stay on (ie battery, handbrake sub tank and a few more). After driving for about 5 mins they all go out and everything appears normal. I put a multimeter on the battery terminals on start up and it read 11.7 volts. After the lights went out it measured 13.9 volts. The battery showed evidence of batttery fluid weeping out thru the cell caps. Additionally I recently had to replace 2 brake light bulbs and one spot light bulb at the 150k service. It sounds like alternator probs; is this right?