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The problem could be with the 9th injector or with the cold-start coolant temp sensor/timer, located in the front of the intake base to the right of the coolant temp sensor used by the ECM.
You can put a test bulb across the 9th injector harness or use a DMM to see if it's being turned on during a cold startup.
From: Sacramento, CA Money can't buy happiness - but it's more comfortable to cry in a Corvette than a Yugo.
It is probably the 9th or cold-start injector. It could however be the cold-start thermal time switch as 65Z01 says. Neither one is connected to the ECM in any way. Since it only happens when cold overnight, I'd say it is due to one of the above and pretty much rule out one of the other 8 injectors, although it could be a very small leak in one of the regular 8 injectors that requires an overnight period to cause the problem. That happened to me.
You cannot buy a replacement cold-start injector anymore. You can have Rich at Cruizin Performance "rebuild" your injector.
The Factory Service Manual has a full write-up on how to test the cold-start switch. It is easy to get to and to test. When I last checked, replacement cold-start switchs were still available for around $20.
Interesting, mine does the same thing, except when it is brutally cold, it will stall once. Anyway of cleaning the ninth injector aside from running FI cleaner through the system, or do they pretty much just fail?