I don't have an Elky CSM, but I have one for an 87 Oldsmobile on hand. This will involve Sensor end ground (Terminal A), a 5v reference source from ECM (to Sensor Terminal C) and the variable signal feed back to ECM (Sensor Terminal B).
Key on, engine off. If you measure the voltage signal across C and B where it enters the ECM, you can do your voltage testing. Is that the testing you did? Terminal A at the sensor goes to ECM terminal 22. Terminal C from sensor goes to ECM Terminal 21, and Terminal B at the sensor goes to ECM Terminal 1. Again, verify the ECM terminals for the Elky ECM.
Measure across Terminal 1 (variable voltage from Terminal B to ECM) and 22 (ground from Sensor Terminal A into ECM). The voltage should vary a bit, and will depend on elevation. <1000 feet you should see between 3.8-5.5V. If you're way up there at 9,000-10,000 feet, the voltage should be between 2.5-4.0V. As you go lower, the voltage should climb.
If the test shows at or over 2.5V, the problem could be intermittent. If <2.5V, then pull connector off of Baro Sensor and use a jumper wire to connect Sensor Terminals B and C. Check across terminals 1 and 22 again. You're sending direct 5V reference signal back to the ECM by doing this.
If the voltage shows between 4-6 volts with the jumper wire in place, this is considered normal full voltage so the baro sensor must be bad. Replace the baro sensor.
If <4 V, check voltage between Sensor Terminal C and ground. If still <4 V, check for a problem in your reference voltage wire from the ECM to Termial C. If the voltage is 4-6V from Terminal C to ground, then the variable voltage wire back to the ECM terminal 1 may have an open or potentially the ECM could be having an issue.
If you need it, the Baro sensor is exactly the same as a MAP sensor (non-turbo). GM p/n 16006845 superseded to 12219931. (Standard Motor Products AS6 if you go aftermarket).