Idling problems are listed for a missing VSS signal (DTC 3-1-1), so it seems you're on the right track. I assume if you were to reset the OBD codes that 3-1-1 would soon come back?

Question 1: When you said you checked the wire on the back of the cluster, I assume you meant the single violet/white wire on the double spade lug (connector D)? That's the VSS signal from the speedometer going to the ECU.

Question 2: Does the speedometer work when driving? If okay then that eliminates the speed sensor and half the speedometer section. If not then check a) for damaged wiring at the rear speedometer sensor (not that uncommon) and then check b) the back of the cluster for connector A (behind the tach) being fully seated and that the brown-white and brown-gray wires (pins 3 and 5 respectively) from the speed sensor look okay and are as seated and fully pushed in from the back as the rest of the pins.

Question 3: In recent history when this problem first happened, had you had the instrument cluster out? Been doing work behind the instrument cluster? Or have the ECU connector off? VSS just happens to be pin 34 on the ECU connector, the very end of the connector, and may be more subject to being bent or damage during attempts to reseat the connector after removal, also if the connector doesn't happen to be fully seated. Inspect the end pins (pin 34) in the ECU connector carefully with a magnifying glass to make sure none of the pin fingers are bent.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now