INSTRUCTOR PLT OF A C172 RECEIVED AN IFR CLRNC WHEN THE ACFT WAS NOT EQUIPPED FOR IFR DUE TO THE ATTITUDE GYRO PLACARDED INOP.

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AFTER WORKING 90 HRS IN THE PAST 5 DAYS AND GETTING MINIMAL (5 HRS) OF SLEEP THE PREVIOUS NIGHT; I CONTEMPLATED CANCELING MY XA30 STUDENT PLT TRAINING FLT; BUT WENT AGAINST MY BETTER JUDGEMENT IN AN EFFORT TO KEEP MY STUDENT ON TRACK WITH THE COURSE SYLLABUS TIME LINE. WE PLANNED TO MAKE A LCL FLT IN MVFR TO WORK ON GND REF MANEUVERS; WITH THE OPTION OF GETTING SOME ACTUAL INST TIME ON THE WAY BACK IF THINGS GOT WORSE ON US. THE FORECAST WAS FOR CLRING; BUT PERSONAL EXPERIENCE IN THIS AREA TOLD ME TO EXPECT THE SCATTERED LAYER TO THICKEN AND DROP DURING OUR FLT. 10 MINS BEFORE OUR LAUNCH TIME; WE ENDED UP SWAPPING OUR IFR CAPABLE ACFT FOR ONE WITH AN INOP ATTITUDE INDICATOR; BUT I FAILED TO MAKE THE SWAP IN MY SLEEP DEPRIVED HEAD. WE ENDED UP GETTING STUCK ABOVE A CLOUD LAYER AS CONDITION DETERIORATED IN A MATTER OF MINS. WHAT CAUGHT ME THOUGH WAS THAT I REQUESTED AND RECEIVED AN IFR CLRNC BACK TO GGS WITH AN INOP AND PLACARDED ATTITUDE INDICATOR STARING ME STRAIGHT IN THE FACE. AS WE SET UP FOR OUR APCH AND WERE FLYING THROUGH A BROKEN TO SCATTERED LAYER; I REALIZED MY ERROR; FOUND A VFR DSNDABLE HOLE AND CANCELED MY IFR SVC TO RETURN TO THE ARPT RIGHT ON THE EDGE OF OUR VFR CLOUD CLRNCS. I DID ADVISE ATC OF OUR PROB AND WAS PLEASED WITH THEIR HELPFULNESS. CONTRIBUTING FACTORS: LACK OF SLEEP! FLYING A LOT OF PARTIAL PANEL WITH MY INST STUDENT THE PAST FEW WKS DESENSITIZED ME TO THE REAL NATURE OF OUR COVERED 'INOP' ATTITUDE INDICATOR AND THE LAST MIN CHANGE OF PLANS. I AM NOW DISCIPLINING MYSELF TO RUN THROUGH THE ARROW AND AVIATE ACRONYMS NOT ONLY BEFORE EACH FLT; BUT ALSO BEFORE ACCEPTING AN IFR CLRNC.