A PA28 ON A TRAINING FLT EXPERIENCED SMOKE FROM DEFECTIVE WIRING. THEY DECLARED AN EMER AND DIVERTED TO NEAREST ARPT.

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PLAN WAS TO COMPLETE AN IFR XCOUNTRY TRAINING FLT FROM ZZZ TO ZZZ1 AND BACK THAT SAME EVENING. COMPLETED PREFLT INSPECTION; RECEIVED CLRNC; AND DEPARTED ZZZ AT APPROX XA00 UNDER DAY VFR CONDITIONS. FLT PROGRESSED RATHER SMOOTHLY AND WITHOUT INCIDENT. AS WE ENTERED NIGHTTIME CONDITIONS; WE CONTINUED THE FLT WITH THE USE OF PERSONAL LIGHTING EQUIP AND OVERHEAD LIGHTING INSTALLED IN THE PLANE AS THE PANEL LIGHTING INSTALLED IN AIRPLANE WAS NOT FUNCTIONING PROPERLY. WE STARTED OUR DSCNT FROM 9000 FT TO 7000 FT WITHOUT INCIDENT AND PREPARED TO BRIEF THE NDB DME RWY 6R APCH INTO ZZZ1. 3-4 MI N OF XXXXX INTXN WE WERE CLRED FOR THE APCH AND TOLD TO DSND TO 6000 FT AND RPT COMMENCING THE DME ARC. IT WAS AT THAT TIME THAT WE BOTH SMELT AND SAW SMOKE COMING FROM THE L SIDE RUDDER PEDALS. WE VERY QUICKLY TURNED OFF ALL ELECTRICAL SWITCHES AND I NOTIFIED APCH CTL THAT WE HAD SMOKE IN THE COCKPIT. APCH CTL ASKED HOW WE WANTED TO PROCEED AND I REQUESTED DIRECTIONS TO NEAREST ARPT. APCH CTL ASKED IF WE NEEDED ASSISTANCE AND IF WE WERE DECLARING AN EMER. I ADVISED THAT WE HAD SMOKE IN THE COCKPIT AND NEED TO GET DOWN ASAP. THEY IMMEDIATELY ADVISED US THAT ZZZ2 WAS 6 MI E OF OUR POS AND CLRED US DIRECT TO AND DSND TO 5000 FT AND RPT ARPT IN SIGHT. AT THAT TIME THE STUDENT WAS INSTRUCTED TO FLY THE PLANE AND I WOULD HANDLE THE RADIOS AND CHKLIST. APCH ASKED FOR NUMBER OF PERSONS AND FUEL ON BOARD AND INSTRUCTED US TO CANCEL IFR ONCE ON THE GND AT ZZZ2. THEY ALSO STATED THAT THE AUTHS WERE CONTACTED AND SHOULD MEET US ON THE GND AND GAVE US PERMISSION TO CHANGE FREQS. IN THE DSCNT TO THE ARPT THE SMOKE DID NOT INTENSIFY BUT RATHER SEEM TO SUBSIDE. THE STUDENT HANDLED THE LNDG AND WE LANDED SAFELY WITHOUT FURTHER INCIDENT. UPON TAXIING TO PARKING WE WERE CONTACTED BY A PLANE OVERHEAD WHO ATC DIRECTED TO INQUIRE ABOUT OUR STATUS. I INFORMED THE PLT TO TELL ATC THAT WE WERE SAFE ON THE GND AND THAT THE SMOKE HAD SUBSIDED. UPON PARKING THE AIRPLANE; I CALLED AND CANCELED OUR IFR FLT PLAN. WE BOTH THEN VISUALLY INSPECTED THE PLANE AND COULD NOT FIND ANY EVIDENCE OF FIRE. AT NO TIME DID ANY EMER PERSONNEL ACTUALLY SHOW UP. WE SECURED THE PLANE AND MADE ARRANGEMENTS TO GET HOME. THE FOLLOWING DAY MAINT LOOKED OVER THE PLANE AND FOUND EVIDENCE OF FAULTY LIGHTING WIRING. IT WAS THIS WIRE INSULATION HAD BEGUN TO MELT. IN REVIEWING THE SITUATION; I AM PROUD OF MY STUDENT AND FEEL THAT WE WORKED AS A TEAM IN ORDER TO HANDLE THE SITUATION. APCH CTL WAS VERY RESPONSIVE AND PROVIDED TIMELY ASSISTANCE THROUGHOUT THE SITUATION. THE ONE THING THAT I WOULD HAVE DONE DIFFERENTLY WOULD BE TO HAVE CONDUCTED A COMPREHENSIVE INSPECTION OF THE ACFT LIGHTING TO MAKE SURE THAT EVERYTHING WAS IN WORKING ORDER BEFORE FLYING IN NIGHTTIME CONDITIONS.