Headlights

If they blink on and off at a fairly steady rate, look for an automatic-resetting circuit breaker in the fuse box. There is one built into the head light switch too, but you replaced that already. You can install a 20 amp fuse in place of the circuit breaker for testing, but put a circuit breaker in there later. It is designed to let the lights come back on after an intermittent overload. That's for safety to allow you to see to safely stop the car. Sometimes the contacts inside the circuit breaker become pitted. The high resistance causes heat buildup in the sensing element. Excessive heat is what trips the breaker. It resets after it cools down.

If the lights flicker rapidly and randomly, suspect a lose connection. The common places to look are for overheated terminals in the switch connectors. Usually the connector body will be melted too.

Caradiodoc

I searched all through the service manual and can't find a convenient test point other than going right to the dimmer switch. Since you already replaced it and know how to reach it, use a clip lead to connect a digital voltmeter lead to the red / orange wire. Ground the meter, then turn it on to the 20 volt DC scale when the problem occurs. If the voltage goes up and down when the headlights do the same thing, move the clip lead to the light green wire and monitor that one.

Caradiodoc

A melting plug can't happen on its own from too much current because ideally, it has no resistance, so there's no voltage drop, and no heat buildup. HOWEVER, undesired resistance WILL cause heat buildup that can melt the plug. That resistance appears at the connection between the terminal in the plug and its mate on the switch, or between the contacts inside the switch. When that happens, both the switch and the offending terminals must be replaced. Typically you'll find two wires in the plug that are hardened for about 4" from being overheated. That 4" of wire must be cut out and replaced, the switch must be replaced, and the overheated terminals must be cut out of the plug and replaced. The entire plug does not have to be replaced. Cut out the melted parts, install crimp-type terminals to the new spliced-in sections of wire, and plug them in individually.

If you don't replace everything at the same time, the high resistance will continue to develop heat and transfer it to the new parts, and the problem will pop up again.