The Click you hear is the Upper AC Board, the furnace relay closing sending the 12 volt signal to the furnace. If you do not hear the click the 2nd time, it may be the AC control board. BUT, the ONLY sure way to tell is to access the 2 blue furnace tstat wires at the AC upper control board and see if BOTH wires have 12 volt positive. If NOT, you have a tstat or upper control board problem. VERY rare. I have NEVER seen that happen. IF both blue wires have 12 volts.-- You have a FURNACE problem, not a tstat problem. Usually, when you must cycle a furnace on and off when it won't relight after first cycle, it is a bad Ignition module board on the furnace. Doug