" I always just assumed that the fuel pump turned on when the ignition was turned on. Does removing the airflow sensor connection improve starting?"

Ted,
The pump is not supposed to run until the cranking airflow raises the sensor plate and opens the Safety Contacts. I guess the idea is to prevent fuel from pumping in case of an accident, but it wouldn't be very effective if you were upside down in a ditch with the key still on. Later systems use ignition pulses to enable fuel operation.

But removing the connector momentarily to "buzz" the pumps might tell you if fuel pressure is an issue in your cold start problem.

If you intend to keep this car or maintain K-jet FI systems in general, I would suggest your first investment should be for a K-jet Fuel Pressure gauge set-up, and maybe the Bosch Fuel Injection book by Bentley Publishers.

Last I knew, the gauge was available from JC Whitney (may be referenced as being for "CI" or "CIS" Fuel Injection) for around $65. The book is about $25.

You could spend close to the same money (maybe more) for a check valve and control pressure regulator and not fix anything.

BTW, I may be remembering this wrong, but I think the Accumulator has as much or more to do with maintaining overnight residual pressure than the Check Valve, whose spec allows as low as 1.7 BAR after just 20 minutes.
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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.