After doing some work on my BL Mazda 3 SP25 (problem also occurs in BK series) that required battery to be disconnected, my a/c began hunting on and off. Plus, everytime it came on, the engine idle would surge to almost 1500 revs. And when the a/c went off, idle would drop to 500 to 600 revs and vibrate. I studied many forum posts which recommended IAC cleans; throttle body cleans; a/c clutch issues etc. I eventually pieced together various bits of info provided in various posts to come up with the answer - which has worked. It all came together when a post said that Mazda engines had to relearn their idle parameters after the battery had been disconnected. One in particular specified that there must be no loads, like the a/c, starting up during the process. I then realised that everytime the battery is reconnected, regardless that you may have turned off the ac prior, the a/c defaults to ON. This meant the learning process was influenced by the start/stop of the a/c. So - this time, I followed the recommended idle relearning procedure. After reconnecting the battery, I turned on the ignition without starting the engine. I turned off the a/c, fan, radio and headlights. After a minute I turned off the ignition. After another minute, I started the engine ensuring no services like the a/c started. I did not touch the accelerator pedal. I left the car idling until the coolant temperature reached 90 degC. It took about 30 mins. Idle was perfect and steady. I stopped the engine. I started again and turned on the a/c. The idle remained STEADY! What's more, the a/c stopped hunting clutch on/clutch off. I recommend you give this a go before stripping parts off the engine. Good luck.