No, the pinion will stay extended for as long as the key is in the START position. That is because the starter drive is actuated by the solenoid. In everyday use it is instinctive to release the key to the RUN position so the starter doesn't stay engaged. There is something inside to let the engine run without wrecking the pinion if still engaged. Like an over-running gear release. I forget what my rebuilder guy called it. Like I said, that bracket often goes missing after the first starter removal. Not uncommon at all. They are on Fleabay pretty cheap though. Looking at the last pic it almost looks like the ring gear is wrong tooth count. Did you ever find out the final history of that car? When was the 350 put in? When was it parked?