The problem I have come across in my past experimentation with simple bridge rectifiers, is in order to avoid the pulsing that inherently comes from this sloppy AC current, you still must run a capacitor in line to "absorb" the pulses. After rectification, obviously, it would then be DC "pulses".
To rectify, and cap a 10w 12v lead to each light... it would be safe to assume that a 12v 15,000uF capacitor would be needed. (Utilizing the general rule of thumb of .0015 F per watt, converts to 1500uF per watt of 12v DC current.)
Just for visualization purposes, Philips manufactures a 12v 14,000uF Capacitor that measures roughly 1.4" in diameter, by about 3 1/4" in length, with two screw terminals. It retails for $6.99.
One of these would be needed per light, in addition to a bridge rectifier capable of an output greater than 860ma @ 12vdc, with a nominal input of 9-36vac. I haven't found anything with a forward voltage of 12vdc+ with such a low AC input. I haven't done a ton of research on this, other than what I've mentioned above, as my lights are intended for DC current, and DC current only. The DC Conversion is such a simple process, that investing in an alternative "bolt on" application would never pay itself back.
Let's face it, lol, a lot of people have trouble with the basic DC Conversion, wiring and soldering in bridge rectifiers and capacitors would be like brain surgery.