Yes, there usually is a chime for headlights on, key off, Drivers door open
Also key in ignition in OFF position, Drivers door open
So have to ask, does the "Door Ajar" light come on with drivers door open, and does the Dome light come on?
If not then Drivers door switch is broken, and fixing it could solve your problem
Or someone disabled the Chime
In any case yes you can use one relay to shut off headlights/parking lights with key off
Fuse 23 in Cab fuse box has 12volts all the time, and it powers the head lights and park lights, also Flash to Pass via the switches
Fuse 6 is the Radio key on power fuse
You will hijack fuse 23 terminals and run them thru the load pins on a 12v 30/40amp relay, use an inline 30amp fuse on the IN to relay
Then tap fuse 6 to activate the relay with Key On
You can just leave the Main Light switch on all the time, or turn it off and on like before it will just go off with key off
DRL would still work with Main switch off, because fuse 23 is on with key on
Automatic headlights need a Light Sensor, which is why you can't just swap in an Automatic headlight switch, you don't have one, FYI
There are several Automatic headlight kits out there, they have the relays and the light sensor
Never tried one, they are not too expensive, which doesn't make me trust them, it needs to handle 10-20amps, lol