Electric choke question
It doesn't have a relay so you won't hear a click. All that's in there is a electric heater element that expands and contracts depending on temperature. When it is cold the element pulls the choke closed and when power is applied (i.e. you start the engine) electricity heats up the element and it pushes the choke open.
Sounds like you have the choke wired to the coil side of the ballast resistor. That's not a good thing because that resistor already gets hot from all the power running through it. Now you've added another power pull on it. That could very well leave you setting on the side of the road (once you get new tires, lol). You should attach the choke wire to the other side of the ballast resistor making sure you have close to 12 volts there. Another reason for this is with the lower voltage source you have it hooked to now will cause the choke to be much slower opening and may cause it to run too rich.