No. The 1999-2004 model year Mustangs do NOT have a separate transmission control module.
The fuel injectors and the COP ignition are "ground start" devices. This means there is a constant +12 volts present the whole time the key is on. The circuit is completed by the PCM grounding the signal return line.
Anytime the PCM calls out a DTC with a "circuit malfunction" DTC it means there's something soooooooo wrong with the circuit that the PCM is unable to perform any trouble shooting.
Have you swapped in a known good COP to one of the positions throwing a DTC? The idea is to see if the DCT follows the device or stays on the original cylinder.
Do you have a test light? To test for a short to ground, put the test light pig tail on battery positive. Probe the device's signal return line. A short to ground will cause the test light to be constantly on.
To test for an open in the signal return lines is what is done by "ringing out" the line. My wiring diagrams indicates that the wire colors do NOT change from what was posted when going through any connectors. Suggest that you double check your work (or you may be looking straight at your problem).
P0351 Through P0360 - Ignition Coil A through J Primary/ Secondary Circuit Malfunction
Open or short in Ignition START/RUN circuit
Open coil driver circuit
Coil driver circuit shorted to ground
Coil driver circuit shorted to VPWR
P1237 - Fuel Pump Secondary Circuit Malfunction
Open or shorted FP PWR circuit
Open FP RTN circuit to FPDM
Open or shorted circuit in the fuel pump
Locked fuel pump rotor
2003 GT Convertible (sold & missed)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.