Administrative Password Required

I have two iMacs both running Catalina (10.15.7). The question involves the newest of the two which was setup using Migration Assistant transferring from the oldest iMac. For the old iMac when I turn on Time Machine I am required to enter my Administrative Password to unlock the icon at bottom left of the screen and check to Automatically engage backup. On the newest iMac there is no lock icon at the bottom of the screen to initiate Time Machine and therefor I do not have to enter Administrative Password. I would prefer to have Administrative Password required for this task. How can I fix this matter. Also makes me wonder if the setup over Migration Assistant did not go as it should, but do not notice any other differences. Thanks for any help.