Q: Recently purchased a used Mazda 3. It sometimes doesn't start and not battery. Believe its the switch / contact in the shifting

There is a neutral start switch and other interlocks that could be at fault. On some Mazda’s with this problem a reported fix involves the plastic shifter cable which can seize to the stud on the switch due to rust on the shift lever. That could prevent full range movement of the shift lever. This prevents the park position from being engaged electronically. You can check for cable seizure and use an appropriate material such as WD-40 or PB-Blaster to try to unseize the cable. This is a known issue and consequently replacement shift levers vended by Mazda have improved corrosion resistance. However, there are other possibilities, too, such as worn out contacts in the ignition switch and loose wiring. The only way to find out is to test these components, that is conduct an electrical diagnostic and a physical inspection of the neutral start switch. If you desire that a certified mechanic resolve this, please request a no start diagnostic and the mechanic will promptly resolve it.