2001 F-150 4.6L Triton. Humming/buzzing drivers side of the engine when engine is off. Drives fine. Have to disconnect battery to stop noise. When reconnecting battery it starts again without key in ignition

 

Something you might consider,

Try removing a fuse on at a time and maybe we can get some idea what circuit might be involved..

There may be a relay panel there too in the driver's side engine compartment. Maybe it is a relay.