I haven't done it myself, but have played with the idea before.
A cheap, effective setup would be
to prevent overcharging the batteries.
It won't be a quick charge by any means, but will work as a float charger.
Also I'm assuming the timer for the unit is one of those twist timers where you use it like an egg timer and it goes off after it gets back to zero.
Is there any reason you can't just like tie it to one side with a string or something to have it constantly on?