Cannot figure out what that part is, but it has a vacuum line connected. Therefore, it should not be functioning unless the engine is running. I would have to guess there is a wire crossed in the key cylinder. The presence of the key should activate the warning system and perhaps deactivate the security system. However, the engine system wiring comes in proximity to the warning wiring behind the ignition switch near the contact reel. It's possible you have a short in that area. I am posting access instructions from autozone.com.
CAUTION
Models equipped with a Supplemental Restraint System (SRS), use an inflatable air bag. Whenever working near any of the SRS components, such as the impact sensors, the air bag module, steering column, and instrument panel, disable the SRS.
- Before servicing the vehicle, refer to the Precautions Section.
- Disconnect battery cable.
- Remove steering wheel and air bag module. Refer to Steering Wheel removal and installation.
- Remove steering column covers. Remove or disconnect the following:
Screws from lower coverClip mounting between the upper and lower coversLower steering column coverUpper steering column cover
- Remove the contact reel:
- Disconnect the left connector.
- Remove the screws.
- Remove the contact reel.
Fig. Removing the contact reel from steering column
Removing the contact reel from steering column
- Remove the ignition switch:
- Disconnect the electrical connector.
- Remove the screws.
- Remove the ignition switch.
Fig. Ignition switch removal
Ignition switch removal
To install:
- Install the ignition switch:
- Position the ignition switch and tighten the screws.
- Connect the electrical connector.
- Install the contact reel. Tighten the M5 screws to 44 inch lbs. (5 Nm).
- Install the upper and lower steering column covers. Tighten the screws.
- Install the air bag and steering wheel. Refer to Steering Wheel removal and installation.
- Connect the negative battery cable.