Bad starter relay?

Hello, been away from the site for some time now but still have my 69 Dodge Dart 340. I have a starting problem with my car that is similar to the above. My Dart has a 727 automatic trans. The relay is of the 2 push on wire connectors type. (yellow wire and brown wire) I checked the yellow wire with a test light and when the key is activated I have a proper connection. The 2nd brown wire going to the trans.was also tested. The probe was placed into the brown wire and the key was activated the engine turned over and fired up immediately. Was this simply because the probe test light made the ground? And therefore I have a bad ground at the trans? Obviously I am a novice at tracking down electrical issues..
Thank you, bob