MitchW

Sorry for a late reply zsmitho, I didn't see any email notification for your comment. 
You've done better than me first time around!
Based on the wiring diagram I found, it indicates that the way you have it wired up would be constantly running through the resistor. The relay for the secondary circuit which bypasses the resistor is not being activated. See photo attached, circled in BLUE you have activated the fuel pump circuit. Circled in RED you have not activated the relay to bypass the resistor.
You could check whats happening at your pump by seeing if you have 12v at the fuel pump, I suspect you don't currently.  If you want constant 12v at the pump (have no need for fuel pump speed control) then I would pair both pins into a single ecu output.
Yeah spot on, I did the exact opposite to you and only activated the resistor bypass circuit, so I had no power entering the fuel pump circuit.

Wireman, AdamW is spot on. The Altezza PnP ecu is the only aftermarket ecu that I know of which supports the Toyota multiplex network.
 
As an update to my original question for anyone interested, it was a wiring problem. I found a JZX110 wiring diagram, and discovered the fuel pump circuit features two relays; the first to turn the fuel pump on but through a resistor (fuel pump runs at low speed), and a second relay to bypass the resistor and allow the pump to run at full speed. My mistake was that I was only energising the second relay to bypass the resistor, not the first relay to energise the whole fuel pump circuit. The relevant pins are E4 (energise the circuit) and E3 (bypass the resistor).