So here is my situation. I will confess, this is not actually a 350Z problem specifically but this forum is very knowledgeable and may be useful for someone else that is running into a fuel pump relay problem.
Please excuse my electronic and relay noobosity. I know I'm making the electronic engineers out there cringe

I have a car with a fuel system that operates at 12v/8v, alternating between the two depending on fuel demand and cruising condition.

This system is suboptimal when trying to run stable fuel pressures and quite frankly some aftermarket fuel pumps don't tolerate it very well. I converted this system to run ONLY 14v to the pump. Here is my general wiring setup:

The OEM pump has two sets of wires. One that presumably carries 12v power from the fuel ECU and one that carries the 8v.
I ran BOTH the output wires together to the coil side of a SPDT relay.
The other side of the relay has direct 14v power from the alternator.
I am using a fairly cheap SPDT Bosch style automotive relay (without a diode).

The problem:
When cruising along and basically idling along (presumably the relay should be receiving a ~8v signal) the relay and fuel pump will randomly shut off (fairly rarely and not easily reproducible). I'm assuming this is due to a voltage drop that makes the coil de-energize and open the 14v circuit. I don't know what the drop out voltage for my relay is specifically but typically I was told these relays will stay closed until the voltage (or amperage??) drops to below ~70% of their rated handling. Meaning, a typical 12v relay should not be shutting off until below ~5v, correct?

How do I fix this circuit so that my fuel pump does not shut off when the fuel ECU switches to 8v? Is it simply a shitty relay? Can a capacitor help?

HELP!

 

The word "noob" does not quite apply to you in this case . You seem to know more than most guys. You just have a bigger problem. Hopefully you get the help you need

 

I would find a lower voltage relay (5vdc) and use resistors to drop the 8v/12v voltage to something lower. I would also install diodes to prevent back-driving the ecu.

If you can't find a 5v relay large enough to handle the fuel pump motor current, you can always drive the relay that you are using now with the 5v relay in a cascaded arrangement.

The size of the resistors depend on the resistance of the relay/diodes chosen. I've attached a spreadsheet that might help with the calculations.

edit:

So I'm bored today. Here's a bill of material:

Qty 1 Allen-Bradley 700-HB32Z06 General Purpose Blade Base Relay, 15 Amp Contact, DPDT, 6V DC $21.04
Qty 1 Allen-Bradley 700-HN153 11-Blade Base Socket, Screw Terminals, Guarded Touch Safe Terminal Construction $18.98
Qty 2 ON Semiconductor MUR260G (Digi-Key #MUR260GOS-ND) Diode $0.51
Qty 1 Panasonic ERX-2SJ6R2 (Digi-Key #P6.2W-2BK-ND) 6.2 OHM 2W 5% Resistor $0.45 (8-Volt control signal)
Qty 1 Ohmite 42J25RE (Digi-Key #42J25RE-ND) 25 OHM 2W 5% Resistor $1.04 (12-Volt control signal)

 

Boom. Head. Blown.

I ordered the list and will be hopefully tackling the issue this weekend. Thanks for the help!!!

 

One caveat. The values for the resistors that I've chosen with this combination are theoretical. You may need to adjust them +/- to get 6vdc for the relay coil -20 to +10%. Do you have a Volt/Ohm meter?

 

I do have one. Yea I will adjust as needed. I actually went conservative on the Ohms and ordered slightly smaller resistors than you recommended but I do have a few small single digit resistors on hand I can throw in series if I really need it.

Also ordered a 68000µF capacitor just because I'm not exactly certain if my voltage cuts out momentarily and that this is the actual cause of my relay drop-out. It was less than $5 and if it smooths out the voltage I'll be happy.
If I do end up using the cap, I was planning to wire it up in series with the coil of the relay. Is there any problem with that? I was considering wiring up two smaller caps in series right before the resistor but couldn't see a reason why a single larger cap wouldn't work instead.

You pdf diagram is AWESOME btw!

 

On the cap, you would not want to wire in series. Caps block DC but pass AC. They also store energy. To "hold-up" the relay coil you would want to wire the cap parallel with the relay coil. Positive end of the cap to the positive side of the relay coil, usually labeled A1 on the relay that I spec'ed, and the negative end of the cap to A2 ground.

The relay itself consumes 50mA. That 68000uf cap may hold it on a lot longer than you would like.

If you use extra trim resistors make sure they are at least 2 watts. I calculated a little over 1 watt on the 12vdc signal.

Thanks for the compliment on the diagram. It's how i make my living.

 

My bad on the relay current. I was going by memory. The relay draws appx. 217mA. Your cap might be allright.

 

I realize you already ordered the parts, but you could have used a single NPN transistor available at radio shack for $.99.

You would wire the base to the trigger wire(s), the emitter to ground, and then the collector would provide your (-) switch to the relay - wire the other side of the relay to ignition power.