The only way the engine can rev up is it must get air. Are you sure the throttle is closed to the idle stop? Is the IDLE (IDL) pin to the ECU grounded by the TPS sensor? I have a US spec 93 LS400 Engine ECU and trans in my 83 Celica and just got it running a few weeks ago. My minor problem is basically the opposite of yours. My cold idle is way too low, but it runs fine once warmed up. I think my idle speed control motor is frozen. Yours may be too, but open instead of closed. The idle motor is on the front of the intake plenum with a hose to the intake pipe right after the air flow meter. When it is revving up high, try pinching the hose closed with a pliers. If the revs come down, it is the idle motor letting in the extra air.
Your diagram is a little too basic to keep the 93 LS ECU from setting codes, but it should run okay. The fuel pump is controlled by a box that was in the trunk of the LS. My US donor car had it in the right rear corner behind the CD changer. It is simple to wire up with just 5 leads. Ignition power, ground, FPC, DI, and Ouput to pump. FPC is the command from the ECU to run the pump at either full or low speed. DI is a signal back to the ECU that it is working correctly.
The LS400 ECU also needs a signal from the brake lights, and the real neutral switch to properly operate the trans. You also need a signal from the speedometer. I was able to use the SP2 sig nal with a divide by 3 circuit to fool it. so far it seems to be working. SP1 should be divided by 5 but the ratio in the trans made this the same rate at the ECU. It worked out to something like 3800 pulses per mile. I also connected switches and lights for the overdrive switch and the power/normal switch. The OD Off switch in the Celica shifter was reverse polarity so I had to use a small relay to make it work as labeled.
I hope this helps.
Gary M.