Short in steering column wiring

remove the steering wheel and then remove the indicator switch assembly

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.

1. Before servicing the vehicle, refer to the Precautions Section.
2. Disconnect battery cable.
3. Remove steering wheel and air bag module. Refer to Steering Wheel removal and installation.
4. 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
5. Remove the contact reel:
   1. Disconnect the left connector.
   2. Remove the screws.
   3. Remove the contact reel.
      
      
      Fig. Removing the contact reel from steering column
      Removing the contact reel from steering column
6. Remove the ignition switch:
   1. Disconnect the electrical connector.
   2. Remove the screws.
   3. Remove the ignition switch.
      
      
      Fig. Ignition switch removal
      Ignition switch removal

To install:

1. Install the ignition switch:
   1. Position the ignition switch and tighten the screws.
   2. Connect the electrical connector.
2. Install the contact reel. Tighten the M5 screws to 44 inch lbs. (5 Nm).
3. Install the upper and lower steering column covers. Tighten the screws.
4. Install the air bag and steering wheel. Refer to Steering Wheel removal and installation.
5. Connect the negative battery cable.

see the diagram attached and proceed according for to fix, use the VOM.
God bless you.

if you hit the horn you should be able to thear the realy click, if not remove the horn pad and groung the wire, if it clicks the steering column has a bad ground, then remove the horn wire, its behind the right headlight unit lower down, and test voltage there, if good check horn ground, if all is good replace horn

Before servicing any electrical component, the ignition key must be in the OFF or LOCK position and all electrical loads must be OFF , unless instructed otherwise in these procedures. If a tool or equipment could easily come in contact with a live exposed electrical terminal, also disconnect the negative battery cable. Failure to follow these precautions may cause personal injury and/or damage to the vehicle or its components.

1. Disconnect the negative battery cable.
2. Remove the steering column trim covers.
3. Remove the retaining screws from the multifunction switch.
   
   

   Fig. Remove the multifunction switch (2) from the steering column
   

4. Remove the multifunction switch from the steering column.
5. Disconnect the electrical connectors from the multifunction switch.

To install:

1. Connect the electrical connectors to the multifunction switch.
2. Install the multifunction switch to the steering column while depressing the spring loaded horn pin.
   NOTE Use the correct fastener in the correct location. Replacement fasteners must be the correct part number for that application. Fasteners requiring replacement or fasteners requiring the use of thread locking compound or sealant are identified in the service procedure. Do not use paints, lubricants, or corrosion inhibitors on fasteners or fastener joint surfaces unless specified. These coatings affect fastener torque and joint clamping force and may damage the fastener. Use the correct tightening sequence and specifications when installing fasteners in order to avoid damage to parts and systems.
   
3. Install the retaining screws to the multifunction switch and tighten the screws to 36 lb inches (4 Nm).
4. Install the steering column trim covers.
5. Connect the negative battery cable.
6. Ensure that the multifunction switch functions properly.

This Is Park Lock Cable Failure here is the Replacment Procedure

Park Lock Cable Replacement

Removal Procedure

1. Disconnect the negative battery cable.

1. Remove the console.
2. Remove the knee bolster.
3. Loosen the lower steering column bracket bolts.
4. Lower the steering column.
5. Place the transmission shift lever in the PARK position. Important: Do not proceed to the next step with the key in any position other than the RUN position.
6. Turn the ignition key to the RUN position.
7. Insert a screwdriver blade into the slot provided in the ignition switch inhibitor.
8. Depress the cable latch. Pull the control cable from the inhibitor.

1. Push the cable connector lock button at the shifter base to the up position.
2. Unsnap the cable from the park/lock lever pin.
3. Depress the two cable latches. Remove the control cable latches from the automatic transmission control.
4. Remove the control cable clips.

Installation Procedure

Important: When installing a new park/lock cable, keep the shipping cover gauge attached until you are instructed to detach it. The shipping cover gauge will aid in the proper positioning of the cable.

1. Ensure that the cable lock button is in the up position. Place the shift lever in the PARK position.
2. Snap the control cable connector into the automatic transmission control.
3. Place the ignition key in the RUN position. Important: Do not insert the cable with the key in any position other than the RUN position.

1. Snap the control cable into the inhibitor housing until the snap lock is seated.
2. Remove the shipping cover gauge.
3. Turn the key to the LOCK position.

1. Snap the control cable end onto the shift park/lock lever pin.
2. Push the cable connector hose forward in order to remove any slack.
3. With no load applied to the connector nose, snap the cable connector lock button down. Important: Inspect for proper operation of the park/lock control cable before installing the steering column to the instrument panel.
4. Raise and connect the steering column.
5. Tighten the lower steering column bracket bolts.
6. Install the knee bolster.

Your going to need to remove the steering wheel and the steering column cover,then you can access the screws holding the "multi function switch",which is the new name for the turn signal switch ,since it does more now.

90 minutes. Steering wheel must be removed.

1991-94 Cavalier
See Figure 5
This procedure covers removal and installation of the headlamp, headlamp dimmer switch, turn signal and hazard switches, as well as the cruise control switch.

1. If equipped, disable the SIR system. For details, please refer to the procedure located in of this repair guide.

Fig. Fig. 5: View of the steering column showing the turn signal switch location

1. If not already done, disconnect the negative battery cable.
2. Unfasten the horn pad, then remove the steering wheel. For details, please refer to the procedure earlier in this section.

If necessary, using locking pliers with a piece of rubber (such as a spark plug boot) between the jaws to help prevent damage to the tilt lever during removal.

1. If equipped, remove the tilt lever from the steering column by grasping the lever firmly and twisting counterclockwise, while pulling it from the column.
2. Remove the upper and lower steering column covers.
3. Remove the dampener assembly, then unfasten and remove the switch assembly from the vehicle.

To install:

1. Position and secure the switch assembly.
2. Install the dampener and the upper and lower steering column covers.
3. If equipped, attach the tilt lever to the column.
4. Install the steering wheel, then fasten the horn pad.
5. If equipped, enable the SIR system, as outlined in of this repair guide.
6. Connect the negative battery cable.

on cavalier and sunfires, the whole dash has to be removed to get the hvac unit out, steering column and all, they easy to get out after the dash removed, you will need a day or so for the whole job. after the hvac unit is out, you have to take it apart, there may also be a access door where the heater core sits that you may pull the heater core out.