Shuey, appreciate that it's not cutting out at the moment, & that it's sometimes a problem with starting, but don't completely rule out the CPS. However, if it was an NB8A then I'd say coilpack.
Can't hear the fuel pump kick in on my NA8 when key turned, but others reckon they can hear theirs on other model MX5s. You should hear the click in the engine bay, as you are doing, which should be the EGI relay. The hum sounds like your fuel pump is working, but the point is though that when it won't start do you still hear the click & hum?
Generally the EGI relay (Fuel Inj relay on the NA) is difficult to remove the first time, which given you suggest yours was not easy to remove, seems to indicate yours has not been removed in the past. Simplest thing to do is buy another relay (2nd hand) - if it turns out you don't need it then you've at least got a spare.
No need for OBD reader as I don't believe your NB8B has an OBDII port - from memory OBDII port was introduced in Aust in 2002. So to check for error codes on an NB8B, see both of Caff's posts in:
viewtopic.php?f=18&t=16872Bit more reading on fault codes for NA:
http://www.miata.net/garage/Engine_Diagnostics.htmlhttp://www.miata.net/garage/faultcodes.htmlOn the NA at least there's also a fuel pump relay under the dash on the driver side (RHD), but these seem quite stable, particularly compared to the EGI relay in the engine bay. If it's the fuel pump then a replacement can be had for under $100 posted to you. If it's the fuel pump wiring then it's just a few $ to fix, but both involve removing the fuel pump & fuel gauge sensor assembly from the top to the tank just under the rear parcel shelf. This isn't difficult but it's critical you do it in an extremely well ventilated area where there is no chance of a spark or flame (pilot light) being near by!
A cheap multimeter can be very handy in diagnosing the fuel pump or fuel pump wiring issue. If a call had to be made on order of likelihood, then it would be: EGI relay, CPS, fuel pump/ wiring.
