Hi, I have my ABS LEDs coming on intermittently also. I suspected the ABS pump too but there are times when it works fine and it could be the a wheel sensor instead. It seems to happen more in drier, less humid weather also and will turn on if the wheels spin.
If you have had any wheel kind of work since it happened, like new tyres or a tyre rotation then it might be worth considering in case it has been accidently bumped and out out of alignment.
From what I understand so far, it is the ABS LED stays on hard all of the time then it might most likely be the pump but intermittently turning on could be ta wheel sensor. Interrogating the fault codes from the engine should
give finer details - is it the pump or sensors or something else etc, but would be nice to get some confirmation on what is busted first up
If it is the the pump, then one option might be these company that recondition your ABS module. They are located in Sydney and I think your mechanic would have to remove the pump and send it off to get the magic done. I haven't used them but it is an option over a dealership $3k pump. Home
Alternatively, you might be able to fish out a pump from a Mazda wrecker like Formaz but of course YMMV and may need a recondition anyhow.
I share your pain on a $3k ABS pump which is even bigger that the $1700 for front discs that a Mazda dealership quoted