Mazda MX-6 idles high and low then shuts off

Vacuum leak, cracked hoses or gummy vacuum hoses.

If your car runs while being boosted,you may have an altenater problem, i just had to change mine. it would not charge battery unless the rev's were up at 2000 rpm at idle no charge

It sounds like that not only is the battery totally dead ,due to a high very internal resistance, but that the alternator has very low output. While car is idling in neutral, the alternator has just enough output to supply the ignition circuits but once in gear and the idle speed drops there is insufficient voltage to run engine so it stalls, It is the same when the lights are turned on as the alternator cannot supply enough to run lights so engine dies without enough drive for the ignition circuits. Try another battery or install a new one. Also have the alternator output checked as it could be the cause of the battery dying in the first place because it has not been maintaining charge as you drive. The alternator problem would be caused by either worn brushes and / or a faulty electonic voltage regulator which is mounted inside the alternator with the brushes.

In a quiet place - such as your garage, turn on the key, but don't start the car. When you first turn it on you should hear a whirring sound from around the fuel tank area. This is your fuel pump. If you don't hear it pressurize your fuel lines then it most probably the fuel pump has gone bad or a fuse is blown. Check your fuses - there usually is one for the fuel pump.

The multifunction switch may be the problem.

my mx6 died on me one day,same thing it would keep cranking but would not fire and start towed to a garage spark tested.NO spark changed distributor and problem fixed

replace idle control sensor.

sounds like the tps is bad or idle control motor

here is what you need to do, a cleaning of the intake throttle blade and the idle speed control air-bypass valve, they get full of gunk over the miles and cause idle issues (stalls) like yours,
Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake

Well, for the battery, sounds like loose cables or corosion on terminals. As for the two idleing speeds, is it carb or fuel injected? If it's carb, it's normal. If fuel injected, not sure off hand.