
You are supposed to be able to unplug the latched piece from the module, see if you can, carefully. I would replace that module and inspect your wiring harness. I got some information on that module from alldatadiy.com:
EDIS module The Ignition Control Module (ICM) is a microprocessor-based device with coil drivers which make decisions about spark timing and coil firing. The module turns the coils ON and OFF at the correct time and in the proper sequence based on information from the Crankshaft Position (CKP) sensor and a pulse-width modulated Spark Output (SPOUT) signal generated from the Powertrain Control Module (PCM) . The module receives CKP and SPOUT signals and produces Profile Ignition Pickup (PIP) and Ignition Diagnostic Monitor (IDM) output signals which are sent to the PCM.
REMOVAL
Disconnect battery ground cable.
Disconnect Ignition Control Module (ICM) electrical connector by carefully lifting up on the connector finger ends while grasping the connector body and pulling away from the ICM.
Remove two retaining screws and remove ICM from bracket.
INSTALLATION
Position ICM to bracket and install retaining screws. Tighten to 3-4 Nm (24-35 lb in).
Connect electrical connector by pushing until connector fingers are locked over locking wedge feature on ICM. Locking the connector is important to ensure sealing of the connector and ignition control module interface.
Connect battery ground cable.
That module has many functions:
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Fix it first, maybe you will have it solved!