Okay, here is an explanation of the fuel pump control relay and fuel pump relay
78 Fuel Pump Relay Notes
There are two relays
1. Fuel Pump Control Relay
2. Fuel Pump Relay
Fuel Pump Control Relay:
Positive coil voltage comes from the white/black wire (Origin is the Ignition Relay)
One coil is grounded through Alternator (blue wire).
The other coil is grounded through the oil pressure switch (yellow/black).
The relay has form C contacts.
A contact puts wiper (white/black) in contact with power from ignition relay.
B contact puts wiper in contact with power from engine cranking (black/yellow wire).
(Note: This is opposite of how it is drawn in the factory wiring diagram, but how it is drawn does not make sense.)
The wiper provides coil power to the Fuel Pump Relay.
Fuel Pump Relay:
Positive coil voltage comes from the white/black wire from the Fuel Pump Control Relay wiper.
Form A contacts connect two green/blue wires. One side comes from a fusible link. The other side goes to the fuel pump.
Theory of operation:
When cranking the engine, within the Fuel Pump Control Relay, the second white/black wire mentioned above is connected to the start position on the ignition switch. This energizes the Fuel Pump Relay and powers the fuel pump.
If the engine starts, the key is released to the ON position, and the first white/black wire is energized from the ignition relay. The blue wire is grounded through the alternator and the coil is energized within the Fuel Pump Control Relay. This closes a set of contacts within the Fuel Pump Control Relay that allows the second coil to energize, provided there is sufficient oil pressure. With the second coil energized, the power from the ignition relay is providing power to energize the coil on the fuel pump relay.
How this applies to your problem:
The odds are that the voltage is dropping on the white/black wire coming off the ignition relay.
List of components fed from the white/black wire from the ignition relay:
Fuel Pump Control Relay
Electronic Fuel Injection Main Relay
Flasher fuse (Green wire)
Fuel Gauge fuse (Blue wire)
The loads off the Flasher fuse:
Brake Warning Lamp Check Relay
Turn signals
Seat Belt Warning Timer Unit
Fuel Level Warning Lamp
Reverse Lights
The loads off the Fuel Gauge fuse:
Fuel Gauge
Water Temp/Oil Pressure Gauge
Tachometer
Process of Elimination:
There are several components here that we can definitely cross off as problematic: Fuel Pump Control Relay, EFI Main Relay, Seat Belt Warning Timer Unit, Fuel Level Warning Lamp, Fuel Gauge, Water Temp/Oil Pressure Gauge, Tachometer.
So IIRC, you said that the car would die when using turn signals or putting the car into reverse. Those are BOTH powered off the flasher fuse in the fusebox, and the flasher fuse gets its power via the white/black wire from the ignition relay.
There is even a common point for these two circuits that initiate the problem: the right rear taillight assembly.
Here is a simple test. Disconnect the wiring harness going to the right rear taillight assembly. Start the car and try to put it into reverse. If it does not die, try turning on the right turn signal. If it does not die, you have confirmed that the issue is at the right rear taillight assembly. You may have to take off the plastic panel to access the connector.