Will EGT Gauge Drain My Battery?

I think you did it wrong

Did you install "electric" gauges? If so the 12VDC "constant" they are refering to is a 12VDC source that is on in the "run" and "start" position. Not a constant (all the time) hot.

What series are you using?

When I did my buddies PSD, we used the add a circuit and used the ECM fuse I think. The gauge needs power when you turn the truck on and start. When you turn the key off the needle will stay at what ever it was reading at that time. The next time you turn the key to "on" the gauge will cycle and then read the present temp. Only should have power when the key is on but also in "start".