It's probably the ignition switch itself actually. It could be the rod but I kind of doubt it. The ignition switch is what the rod goes into and actually moves to engage connections. If the switch is worn out then this is why jiggling it might sometimes make it work.
All you have to do is remove the column plastic that hides it and it should be very self evident. I think there might be a small amount of adjustment that the switch will have to mount to so before you put the plastic back on make sure that it's in proper adjustment and it starts.
There's also a PATS transceiver in the column that sends out a signal to the key and gets a signal back. It's rare but perhaps that's the problem.
All you have to do is remove the column plastic that hides it and it should be very self evident. I think there might be a small amount of adjustment that the switch will have to mount to so before you put the plastic back on make sure that it's in proper adjustment and it starts.
There's also a PATS transceiver in the column that sends out a signal to the key and gets a signal back. It's rare but perhaps that's the problem.