Windstar Possessed by Gremlin (NOT the AMC kind!)

Hi Kids! We have a 2001 Windstar which has recently been misbehaving. Has anyone encountered these symptoms?

-message center sometimes works, sometimes doesn’t. it either works 100% or is completely black.

-left headlight was flickering, then went out. no corresponding message in message center.

-replaced headlight bulb @ dealership

-dealer could not find message center problem, as luck would have it, it was working fine.

-dealer said battery needed replacing - so, we did.

-2 days later, new battery was stone dead.

*any opinions on whether the message center and battery death are connected?

*if it’s a parasitic draw - any ideas as to from where?

Thanks very much for your input.