Yo T,
Do you have the oxygen sensor code number?
Just asking even though the oxygen sensor is Not likely the stall and no start cause.
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I tend to agree with the mechanic because;
Ignition Control Module (ICM) (Ford) General Descriptions; "...A major cause of failure is heat... especially typical on Ford, is intermittent failure. The car runs okay for a while, then stops. When it cools, it runs okay for a while longer. Then it stops again. And so on. This is a fairly certain indication of a heat failure fault which can be prevented from recurring by re-locating the ICM to a place away from the engine. See article below.
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As Bob and your mechanic advised, test for spark when it stalls and won't run;
Ignition Coil Secondary Voltage Test
Coil Voltage Test #1 - Crank Mode
http://www.therangerstation.com/tech_library/images/TFI_sparktest.gif
1 - Connect a spark tester between the ignition coil wire and a good engine ground.
2 - Crank the engine and check for spark at the tester.
3 - Turn the ignition switch OFF.
4 - If no spark occurs, check the following:
a. Inspect the ignition coil for damage or carbon tracking.
b. Check that the distributor shaft is rotating when the engine is being cranked.
c. If the results in Steps a and b are okay, go to Test #4.
5 - If a spark did occur, check the distributor cap and rotor for damage or carbon tracking. Go to the Coil Voltage Test #2
http://www.therangerstation.com/tech_library/TFI_Diagnostic.shtml
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Btw, Stator and TFI both share the same grounds and power circuits, when one fails the other might be bad as well. Its a standard practice at dealerships and most quality repair shops to replace the TFI and stator at the same time. This prevents the problem from re-appearing a few weeks later. by Ryan M
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ICM Relocation; on a Ranger/Bronco II.
http://therangerstation.com/tech_library/remote_tfi.htm
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FYI "...Ford calls this electronic ignition the Thick Film Integrated-IV (TFI-IV) ignition system. The TFI module is also known as the Ignition Control Module (ICM) which reports engine position and rpm to the PCM. The PCM then determines the proper spark timing and advance, and returns a reference signal to tell the TFI module to switch the coil, thereby creating a spark. The PCM used on these vehicles is referred to by Ford as the Electronic Engine Control-IV (EEC-IV) module.
GL!