as already mentioned, if you can tap the switch and the lights flicker on turn on temporarily, then its most likely the little plastic bits which push the contacts open and closed in the light switch. its very easy to spot them once you open the switch, they are in a line of 3 and are spring loaded. The one that has melted (either just cus nissan miscalculated current draw with age/ higher wattage bulbs used/ or accessories being run from the light circuit ie gauges) is pretty obvious to see, what i did for a temporary measure was to trim the melted bits off as it tends to mushroom at the top, then grabbed the spring and stretched it out a bit more to make up for the part that melted, then reassembled it and checked continuity at the plug. Sure this solution isnt long term if your setup remains identicle, but it is free and the switch is not hard at all to take apart and reassemble. just wish id taken fotos for you lot.