1999 Dodge Caravan Engine will not turn over, starter repla

I have replaced the starter but engine still will not turn over. If I take a jumper wire from battery cable post on the starter to the electrical terminal on the starter, it will turn over & start. Basically it is a piece of bare wire used to jump it across. I have checked the neutral safety switch with ignition switch turned to the start position, a light tester does not light up when I touch the electrical terminal on the starter with a good grounding, but my reverse lights will light up when gear shift lever is placed in "reverse" position. How can I perform an in car check of the ignition switch to see if it is bad?
Thank you!
Kevin.