This 2.0 Litre 4 cyl. has an issue starting. It clicks when you turn on the key and although the engine turns over it wont start. Yet if you leave the key in the in position, with the starter not engaged, and let the clicking continue until it stops, maybe even 5 minutes worth, then it will start up and run. It might have some hesitation for a while but eventually that goes away. If you turn off the car the same issue may present itself, depending on how long the running time was. It seems to me that this is relative to fuel bleed off in the fuel injection system and that the fuel pressure that is required is failing. No local mechanics seem to have a clue and Mazda wants to pretend ignorance have the car for infinite testing which I cant afford. Any help would b appreciated. Thank you
Have you been able to determine where the clicking is coming from?
If you are looking at the pressure regulator you notice one end is gas in ,on the side it bolts to injector tube, at the top at 90 degrees is a vacuum hose tube. Follow that vacuum hose and you get to what I’m guessing is a vacuum solenoid with electric fitting. This is mounted on top of the manifold in line with 2 others all 3 look identical to me. Looking at the engine, the one on the right is clicking. The wires are white/red stripe and black with looks like light blue stripe.The funny deal is that there are other parts that i think are also clicking. One of them is under and behind the manifold with what looks like 6 wires to it . I think one of the other selenoids is also clicking.When the thing is clicking it seems to transfer through the manifold.
If it is indeed a vacuum solenoid, there’s a good chance it is controlled by a relay, which might be that other clicking. I’d get the multimeter out and start checking those wires for repeated pulses. Could need a new relay, or could be that relay is getting false info from somewhere else. Wish I could help more, but I’m not a Mazda expert 
I changed the main relay, the one that was controlling the solenoid, no change. By the way, the car has been plugged to 3 different scanners all no code.