Somehow I expected after listening and fast forwarding a bit, then ejecting and re-inserting the tape it would retain the tape position, but instead it seems to reset back to the beginning.
That is actually a great idea - authentic and irritating. Just be thankful I never implemented my original plan to have only one copy of each tape in the library. If someone else was playing the tape you had to wait and unless they rewound manually you got to start wherever they stopped.