Push the car and put it in gear it will start?

A friend is moving to another state and towed this car to me to sell it after fixing it. Basically he started having issues with it with regards to starting. It's manual, if he pushes the car and put it in gear it will start, but when you turn ignition on and try to start it, it won't turn over. I read the codes and they were all over first because the battery was disconnected and car was parked. He said the starter connector is loose. I checked it and you can easily remove it and connect it without hearing a click as I think the tab is maybe broken to lock it in place. I tapped the starter with no success. I want to see whether the wire has any signal first, I can't remember whether this wire has one or 2 wires, when should I see a signal? Upon starting or as soon as ignition is on? Also, is it possible the clutch pedal switch has an issue?