I would think that is multiple problem locations.
Assuming the battery is 12.5 volts with the light switch on (Check this), then with the connector to the headlight unplugged, the voltage should be very close to 12.5 V. If with both headlights unplugged there is no voltage, then there is a break in the circuit. It could be non-function dimmer switch or an actual break.
However with the lights not functioning, if the battery is 12 V, the power at the dimmer switch should have been 12 Volts.
Votlage only drops when current is flowing through resistance. So my next question is what did the ammeter show?
If current is flowing and it’s not going to the headlights, then there is a short of some sort.