Stop in for a cup of coffee
And you understand that current is flow.
Like water floooooowwwwwwing in a pipe.
:)
Try drawing arrows representing flow and it shows why the ammeter does't show current with engine off, lights on.
See?
The current doesn't flow through the ammeter getting to the headlights because the gage is in the alternator output line; and alternator output is zero.
Everything will measure 12 Volts give or take, so a voltmeter isn't very helpful in solving this one. Its either eyeballs and tear everything apart, or eyeballs and an ammeter.