It could still be the ignition switch as the section of the switch that runs the starter is a different set of connectors that powers the coil. I'm not sure the signal lights are connected to the ignition switch but again, there are several terminals on that switch. I agree though, based on the starter turning the ig sw sounds unlikely but it still could be the problem. Otherwise, it sounds like it may be a wire or connection between the ignition switch and the coil. Check for frayed wire ends or a dirty/corroded connectors.