Ditto on the wiring connectors. Most miata issues are caused by old wiring that appears to be intact but upon closer inspection, there is a break at the connector. It will probably be the sensor at the back of the cylinder head. The miata motor is merely a detuned GTX.
Well, no. It's not. It's a B6 engine that's been reworked for naturally aspirated horsepower, while the GTX was a B6 engine that has been reworked to swallow boost. The cam sensor on the Miata engine isn't found on the GTX, the latter uses a distributor. A car with a broken wire to the cam sensor usually won't start at all, and won't have fuel or spark.
I had a very similar issue on my Toyota. Same basic Bosch-type VAF. In my case, it turns out that there was a ground missing, which completed the FP-signal circuit in the VAF. The pump would work in the 'start' position, but when back to 'run', since the circuit wasn't grounded, it killed the pump.
I'm not sure about the BF-series GTX, but the BG 4WD setups had a fuel-pump controlling box under the driver seat, since there were two pumps, one on each side of the driveshaft hump in the tank. The control circuit was essentially a timer delay circuit for one side. Maybe something got cut/pinched/jostled/disconnected??
--sarge