Its rated for 2 amps at 125v AC I believe. Im sure this switch will be just fine for what he is using because lowering the Voltage will increase the amp rating.
BatteryStuff Tools | AC to DC Amperage Calclator Through An Inverter
Good website to look at. So at 12volts DC it will work for 23 amps. Being your running at roughly 4 volts it should be even higher
Your switch is not an ac to dc inverter... the tool you posted is useless.
"DC Rule of Thumb
For those switches that list an AC voltage rating only, the "DC Rule of Thumb" can be applied for determining the switch's maximum DC current rating. This "rule" states the highest amperage on the switch should perform satisfactorily up to 30 volts DC. For example, a switch which is rated at 10A 250VAC; 15A 125VAC; 3/4HP 125-250VAC, will be likely to perform satisfactorily at 15 amps up to 30 volts DC (VDC)."
Source:
Amp Ratings, HP, Volts | carlingtech.com
You can assume that your 2 amp 125 volt AC switch would be about equivalent to a 2 amp 30 volt DC switch.
What is the lowest resistance coil you are firing? With the limitations of your switch, 2 amps, it needs to be at 2.1 ohms or above.
Also, to be a picky pete, you used black wire for your positive connections and red for your negative ones.