PCM/BCM/TCM pinout needed?

Constant 12 volts to the violet wire that connects the coils is normal. The ECU controls the coils by turning the ground to each coil on and off. In your case it sounds like the driver transistor that is supposed to control #4 has shorted and is holding the ground on or the control wire (green w/violet stripe) has shorted. I would start by following the harness from the injector and be sure that it hasn't rubbed through and grounded out that way. Next go to the PCM and find the same wire at terminal 2AX There will be a short connector harness with a white wire w/green stripe that you should be able to disconnect. Then test the wire that goes to the coil with a meter set to ohms. If the wire now shows open circuit when tested and unplugged at both ends the PCM driver is likely the culprit, it's actually common for them to short and a burnt coil is the result.