OK, well let me tell you while I ask you that question.
Lets say you have a poor connection before the ignition switch (in the feed). Your true voltage does not show up without any current draw. So if you had 12 volts at the input of the switch without any load and you turned the key to start and it dropped to the same 9 volts you see on the output of the switch, then your bad connection would be in the feed to the switch. You WILL see a small amount of drop but not to 9 volts if everything is as it should be.
Replacing the purple wire based on your previous description sounds like a good idea. But that is not causing the 9 volt problem. You either have a bad switch or you are not getting a good feed to it.