You are on the right track with the resistance theory. Just don't immediately assume the part itself is the cause; it could be as simple as crud in the connector.

Pin it down by measuring the resistance at the ECM plug. With the car off, the key in your pocket, pull the plug off the ECM. Hold it so the wire comes out the top and the business end faces you. Count the pins from the upper right 1-18 and from the upper left 19-35. Ground one probe of your ohmmeter and gently touch your other ohmmeter probe to pin 13 and read something like 5000-7000 ohms if its 40 F outside and cold motor - less if you've warmed it some. When your Bentley arrives, look on page 241-14. It applies to the Bendix in this case too.
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-K (hope springs eternal)