Also if you will notice, there is a thin strip that goes between the two terminals, per thermostat/ECO. This acts as a fuse, and burns up to protect the wiring from burning up as it cut's the power. You will notice in the pic above that the 120 volt AC t'stat/eco switch (the left one) has this fusible link burned up.
You may can check that part also for your 12 volt DC t'stat/eco.
2011 Flagstaff 831 RLBSS
I used to be addicted to time travel, but that's all in the past now.