This article is from the Chrysler-Plymouth-Dodge FAQ, by Dr. David Zatz with numerous contributions by others.
With regard to funny electrical things (in this case, the rear window
washer or rear wiper coming on) when starting a vehicle, or the vehicle
acting like it has a low battery, Ken Bessler <(e-mail address removed)>
The problem is one of two things: your ignition timing (no - really!) is
just a hair too far advanced or you battery is getting old. When ignition
timing is too far advanced, the engine tries to fire before the piston gets
all the way up. The piston tries to go the wrong way, fighting the starter
and causing a big voltage drop across the whole van. This messes up the
logic circuits. Listen to the way your engine cranks over before it fires.
This sound should be fairly even and smooth. If not, back your timing up a
bit. If your engine turns over smoothly, then your battery is suspect.