Does it have to be an AC to DC converter or rectifier and not just a voltage regulator? A lot of motorcycle and lawn mowers have generators that produce AC output then regulate it to 12 volts AC to power lights for instance. They will add in a rectifier if they need to re-charge a battery with 14 to 16 volts DC. That string of lights only needs 9 volts to 12 volts of any voltage AC or DC to light from the 110v/120v AC that's available. Never saw a voltage regulator that small but electrical tech has advanced. My guess is it's a voltage regulator that regulates AC to 9v or something down to under 15v? Can you check if it's AC voltage on the in side and what type of voltage on the other side? If it's AC on both sides then you'll know.