Problem with 1999 Mustang...Fuel Pump or PATS?
The first mistake you made was taking it to a Dealership instead of a reputable independent shop! The dealerships hire "kids with tool boxes" these technicians are fresh out of trade school (they hire them because they don't have to pay them much) and have none to very little hands on experience and a few weeks of factory training (not enough)! Sorry if I got carried away! Now to answer your question, This problem is very common on the PATS system and 9 times out of 10 it is the PATS transceiver and or it's wiring!
1. Perform self-test of the HEC (Hybrid Electronic Cluster) through the scan tool.
2. If code B1681 is present from the HEC's KOEO (Key On Engine Off) On-demand self-test, access the transceiver located just forward of the steering wheel under the ignition switch tumbler area and check the circuits at the connection.
A. A White/Light Blue (WH/LB) wire provides power to the transceiver with the key in the Run position from fuse #34 (20 amp) of the CJB (Central Junction Box)
B. A Black/White (BK/WH) wire provides the transceiver a constant ground.
C. With the key in the Run position, check the Grey/Orange (GY/OG) wire and the White/Light Green (WH/LG) wire for voltage with the transceiver disconnected.
It is not important that a specific voltage level be present on either of these two circuits other than that the circuits show something other than 0 volts, which could suggest that one of the circuits may be open or shorted to ground.
3. If the circuits of the transceiver check to be OK and the connection appears to be in good condition, replace the transceiver and re-check the startability of the engine. Clear service codes from the HEC and PCM.