After driving it around for 10 min I came back and notcied the sound when you first turn your key once, the sound stayed on for a long time even after I started the car. Like the buzzing noise..and when I click it back after the car is started already to the first position the car is still on..do I need a new ignition or can someone please help me if this is normal for these old cars? I attached two videos of it and if you listen you can hear the buzzing sound evn when the car is running.
Autel MaxiSys Pro Scan Tool

 

Can not hear video

Are you saying the starter stayed engaged?