I have an 06 Dakota ST with the 4.7L with 100k miles. I've known for a while that there's a very slow coolant leak from the water pump. Very slow, never caused an issue as long as I keep the coolant topped up.
I was driving today when the battery light came on. It's an old battery, so not too surprising. In very short order the truck started overheating, to the point where the radiator cap vented.
Since it had a mechanical fan, how are these two related? I'm at a loss and I really don't want to just start throwing parts at it.

 

It's not throwing parts at it if you know there are components that need to be replaced. Replace the battery and the water pump. Go from there.

 

I should have clarified. I'm intending to fix those. What I'm trying to figure out is how the two are related. There's no obvious connection that I can think of.

 

Probably not related. Just coincidence.

 

If the waterpump is seizing, then the serpentine belt could be slipping, which could be causing the alternator to not spin enough, which could make the battery drain more then it's being charged making the battery light come on.

did you notice if your power steering or AC is not working as good as usual? that would be other symptoms if the above is what is actually happening.

This is but one scenario that could make the battery light come on with the failing water pump. There could be hundreds more examples.

I agree, it's most likely coincidence, but without knowing more details (age of the battery, where the leak is coming from, etc..) or actually seeing the truck, a forum can only give possible answers.