The PIP sensor inside the distributor isn't easy to test without an oscilloscope engine analyzer. It can and will cause strange problems.
From the Cranks OK, but No Start Checklist for Fuel Injected Mustangs - see paragraph 1 B
B.) PIP sensor in distributor. The PIP sensor supplies the timing pulse to trigger the TFI and injectors. A failing PIP sensor will sometimes let the engine start if the SPOUT is removed. See paragraph 5A – Using a noid light on the fuel injectors will tell if the PIP is working by flashing when the engine is cranking.