So you say it takes from 20sec. to 20 min to restart? Are you trying the whole time for the 20 min or just waiting 20 min?
Here are my thoughts. I have had a simular issue with a diffrent car, I found it to be the ignition switch. As the keys swung around the contacts would intermitanly break killing the car.
If the ecu looses power it will not record any error codes...
http://www.gnttype.org/techarea/imag.../ecm_turbo.jpg
You could put a meter on I blieve pin A6
AT the ecu Pink with black stripe and check the voltage, this electrical print is hard to read poor quality scan. But it looks like pin A6. and when the car dies don't touch any thing check the voltage here. There are some other points I marked on the print that might be worth checking WHEN the car dies. Giggle the keys around and
slightly move the ignition switch back and forth while in park and see if the car dies. Also it helps the use a small diameter needle to poke through the middle of the wire to gain acces to that wire.
Because it only takes somtimes 20 seconds to restart it sure sounds like a bad connection or intermittant contact like the ignition switch and not like an electronic componet. Another area where I have seen my gn have electrical issues, was at the bulkhead connector that
plugs into the back side of the fuse block. The terminal for my fuel pump hot wire had a bad connection here.
Connector Pinout Diagrams