Probably a bad connection at the source of 12 volts.
When there is no load, wire disconnected, 12 volts will be there, no current draw. Connect the wire, heavy load, not enough current to handle the load, lower voltage.
May also be a bad choke cap. However, a quick check would be to hook cap independently to the battery and see (feel) if it gets hot and opens the choke, If it does, then you know it is the source of 12 volts.
I'm sure you're not using the ignition wire, hopefully, your using a switched 12 volts from the ign switch or fusebox.