I performed a bunch of tests on the Central Locking Pump / Security System Module (CLP/SSM). I found multiple tests that failed. I am referencing pages in the 2004 Chrysler Crossfire Service Manual. The following are tests I performed that Failed:

CLP/SSM Undervoltage (8Q-2), Test 4. Voltage of the Fused B(+) circuit (cavity 4) at the CLP/SSM C2 herness connector. Is voltage above 11 volts? Yes >> Replace the Central Locking Pump / Security System Module. My voltage reading was 12.08

CAN B Bus (+) Circuit Failure, Test 3. Measure the resistance between ground and the CAN B Bus (+) circuit at the CLP/SSM harness connector. Is the resistance below 10k ohms? No >> Replace the Central Locking Pump / Security System Module. I was unable to get any resistance reading from the Multimeter.

I am going to order a replacement CLP/SSM and see if this resolves the issue. I'll update the post if this is the solution.