That's what it sounds like.

There's a thread below here I accessed about a week ago, should help you out running the new wire. I think this is the exact same issue you are seeing now.
Starter Wiring

You'll probably have to drop the starter to get to it. If you do, when you pull it out, make sure you don't lose the shims. You'll want to make sure you put those back on when you reinstall! Also, if you have never pulled a starter before, they are extremely back heavy. I killed my last one when it slipped out of my greasy hand and smashed the selenoid on the garage floor. Biggest waste of $45 ever.