For 12vdc you might consider just using mosfets. I'm not sure triacs are appropriate here? I believe they're mainly for AC voltages, and have some particular switching properties... "Once triggered, the device continues to conduct until the current drops below a certain threshold, called the holding current." Basically, depending upon the load, once they're triggered they can stay triggered. Drventure, you were switching AC for the EL wire right? Did you run into any issues with the holding current? Perhaps the wire draws so little current that they were below the holding current and the triacs were allowed to close.
SSRs are fine, especially for AC voltages, but many of them are actually composed of mosfets anyway. If you just want to control a 12vdc from 5vdc logic then I think a single mosfet would be the way to go, and run less than a buck a piece.