GTA Turbo ECU problem

You should be able to check the internals of the oil pump while the engine is still in the car. I am pretty sure Lee has had to do this before.
You will need to remove the exhaust, the crank pulley and then timing chain cover.
look forward to hearing on progress.

It's all doable in-situ but yes the silencer needs to come off + crank pulley which may be a pita...you will need to lock the crank etc.
Oil pump runs in the block and is easily damaged so best to remove spark plugs and oil filter, prime the pump via the oil filter port and just crank till it flows...It's a bit messy but safest way to determine if you have a major issue.

Best to give me a call if you like. Is it an original engine or has it been rebuilt?

At this point I stopped, because the oil pressure gauge shows nothing when cranking (after initial kick when ignition switched on), and the OP warning light stays solid. Maybe the sender or gauge is bad, but a test gauge on the pressure switch feed also shows nothing, and when I left the hole open, no oil appeared. So I think the oil pump is US.

You can test the oil pressure light switch and and oil pressure sender circuit without running the engine.
But firstly ..... your comment ..... " the oil pressure gauge shows nothing when cranking (after initial kick when ignition switched on)" ...... I am just wondering if the gauge you are seeing this happen on is the OIL LEVEL gauge ........ that is the third one from the left of the gauges ...... it has wedge image on the gauge. If this is the one you are seeing kick when you switch on the ign, then that is what it does.
The center gauge is the oil pressure gauge, and of course, the one on the left is the coolant temperature gauge.
Now to check the oil pressure lamp circuit ..... there is a twin connector fairly close to the switch and pressure sensor where you can unplug both these units individually. Follow the wire from the switch to the connector and unplug it and with the ign on, the lamp should be extinguish and only come on when you earth the wire.
Do the same with the sensor wire but as the wire is touched to earth, the oil pressure gauge needle should swing to the right.
If all this checks out, the do as Lee says, and prime the system ......... remembering that not only has the oil galleries got to fill, but the oil filter also has to fill ........ this will take time when cranking.

Thanks for your help. The oil level gauge works fine - goes to full scale for a few seconds, it's definitely the pressure gauge is not moving. The gauge, sender or wiring may well be faulty, but as I said, a mechanical test gauge shows no pressure either. The engine had been partly stripped and partly reassembled when I got it, so maybe they left off the oil pump drive chain or something. But good to know it's possibly doable in-situ.
Once I know there is oil pressure, I can check if the gauge or light need fixing.

The engine had been partly stripped and partly reassembled when I got it, so maybe they left off the oil pump drive chain or something.

I think the chances of the chain being left off the oil pump is pretty remote, but if the engine has been taken apart and the pump removed or just cleaned out, the chances are that the pump cannot suck up the oil from the sump as cranking is comparatively slow and air is escaping around the pump gears .......... this is a common problem. That is why a reference to priming the pump after engine reassembly is important and mentioned in the manual ....... see pic below.
As Lee has previously suggested, remove the plugs and the filter .... prime the pump as directed below with about a small cup-full of engine oil from an oil can, and refit the filter, then crank whilst watching the oil gauge and light. It could take a reasonable length of time for the pressure to build up due to the slow cranking of the engine.
This is an easy procedure to do and worth trying before you start pulling the engine apart.

Oil Prime.JPG

I doubt the chain is missing but there are a couple of other gotchas if the engine has been apart to any great extent. Prime the pump and crank with plugs out. Disconnect the turbo oil feed pipe and see if you get any flow there. That's my preferred test on a rebuild before firing up.

Great idea - I wasn't aware of the priming "trick". Could save a lot of time and knuckles. Back to it next week.

Back to it at last! No joy after much priming of pump.
Just removed sump to check pick-up/strainer, which appears OK, but strangely does not have spacers as shown in the parts book or Simon.de catalogue for the Z7U-730 motor (the engine no. is 6495). The bracket at the strainer end is much taller than shown, and ends 6 cm above the top of the strainer, so I'm guessing this is a revised design to get rid of the spacers and one O-ring. It's definitely dipping in the oil, so it shouldn't be a problem. So one last try once I've found a new O-ring, then it's out with the pump.