Do my car have Theft Deterrent System or Double Locking? Thank you!

Yes they do

https://www.google.com/search?q=2012+chevy+traverse+service+theft+deterrent+system

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Content Theft Deterrent (CTD) Description and Operation When armed, the content theft deterrent (CTD) system is designed to deter vehicle content theft by pulsing the horns and exterior lamps for approximately 30 seconds when an unauthorized vehicle entry is detected. However, the CTD system does not affect engine starting.
An unauthorized entry can be any of the following with the CTD system armed:
• When any door is opened without first being unlocked using the UNLOCK command from the keyless entry transmitter
• Unauthorized entry into the underhood area (if equipped)
• Unauthorized entry into the rear compartment
• After a battery reconnect, if the battery was disconnected with the CTD system armed
The components of the CTD system are:
• Body Control Module (BCM)
• Remote Control Door Lock Receiver (RCDLR)
• Security indicator
• Door ajar switches
• Rear compartment lid ajar switch
• Hood ajar switch (if equipped)

Arming the CTD System
Use the following procedure in order to arm the system:
Place the shift lever in P (park).
Turn OFF the ignition.
Open any door.
Important: The system is not armed if the doors are locked manually; the remote keyless entry transmitter must be used to arm the content theft deterrent (CTD) system.
Lock the doors using the LOCK button on the transmitter. The system is in standby mode and will not start the arming timer until all doors are closed.
The system will begin the arm sequence immediately after the last door is closed. If the keyless entry transmitter is used to arm the system after the vehicle doors are closed, the arm sequence will begin as soon as the LOCK command is received by the transmitter.
Locking the Vehicle Without Arming the CTD System
Locking the vehicle may be accomplished without arming the content theft deterrent (CTD) system. Use of the manual door locks or using the key to lock the doors will lock the vehicle, but will not arm the CTD system.
Disarming an Armed System/Silencing an Alarm
If system arming has been requested by the keyless entry transmitter, it must be disarmed.
Important: Using the power door unlock switch or manually unlocking the doors does not disable the content theft deterrent (CTD) arm mode. Also, disconnecting the battery or pulling fuses does not disable the arm mode, since the BCM stores the CTD mode status in memory.
• To disarm the CTD system in standby mode, perform one of the following:
- Press the UNLOCK button on the keyless entry transmitter.
- Insert a valid key into the ignition and switch to the ON position.
• To disarm the CTD system in the armed mode (non-event) or when activated (during an alarm event):
Press the UNLOCK button on the keyless entry transmitter.

When you first turn on the key the security light doesn't come on ? Is this what your saying ? You don't reset anything , you look at factory service repair manual for diagnostic steps to take to find the problem . And if you don't have factory service repair manual info. you take it to someone you does . Dealer .
Security Indicator Inoperative
Step
Action
Yes
No
Schematic Reference: Theft Deterrent System Schematics
Connector End View Reference: Theft Deterrent System Connector End Views
1
Did you perform A Diagnostic System Check-Theft Deterrent?
YES - Go to Step 2
NO - Go to Diagnostic System Check - Theft Deterrent
2
Observe the instrument cluster.
Turn the ignition switch to the ON position.
Does the SECURITY indicator illuminate during the bulb-check?
YES - System OK
NO - Go to Step 3
3
Replace the instrument cluster. Refer to Instrument Cluster Replacement in Instrument Panel, Gages and Console.
Did you complete the repair?
Go to Step 4
--
4
Operate the system in order to verify the repair.
Did you correct the condition?
System OK
Go to Step 2

have you put obd11 scanner on it to find error code.
DTC P1626 Theft Deterrent Fuel Enable Signal Lost
Circuit Description
The Vehicle Theft Deterrent (VTD) system is incorporated within the body control module (BCM). The powertrain control module(PCM) monitors the state of health serial data message from the Theft Deterrent system to ensure that the PCM to BCM communications is established. If the PCM detects a loss of the state of health message while the engine is running, DTC P1626 will set. DTC P1626 can cause a no-start condition or normal operation depending on when the loss of Theft Deterrent system communication was detected. The engine will continue to start and run if the condition that set DTC P1626 occurred after the PCM received a valid theft deterrent password from the BCM and already allowed fuel during the ignition cycle. The engine will start and immediately stall if the condition that set DTC P1626 occurred before the PCM received a valid theft deterrent password. With this condition present, the PCM will inhibit fuel delivery and disable the starter until a valid theft deterrent password is detected. Refer to Content Theft Deterrent (CTD) Circuit Description .

Conditions for Running the DTC
The Theft Deterrent system has allowed fuel delivery.
Conditions for Setting the DTC
The PCM has detected a loss of the state of health serial data message from the Theft Deterrent system.

Action Taken When the DTC Sets
The PCM stores conditions which were present when the DTC set as Failure Records only. This information will not be stored as Freeze Frame Records.

Conditions for Clearing the MIL/DTC
The DTC becomes history when the conditions for setting the DTC are no longer present.
The history DTC clears after 40 malfunction free warm-up cycles.
The PCM receives a clear code command from the scan tool.
Diagnostic Aids,
An intermittent may be caused by:

• A poor connection

• Rubbed through wire insulation

• A wire broken inside the insulation

Check for the following conditions:, • Intermittent short circuit on the serial data circuit -- Refer to Data Link Communications Operation in Data Link Communications. Be sure to check all related wiring for an intermittent short to ground or short to voltage.

• Poor connection -- Inspect the wiring harness for damage. Check for an intermittent short or open circuit in the wiring harness related to the BCM, including the ignition, battery feed, ground, and Serial Data circuits.

You can't by-pass this system. Try locking/unlocking the doors with the key fob. If that doesn't work, try locking/unlocking the drivers door with the key. If still no luck, try disconnecting the battery for a minute or so. Do you have another key you can try?

It's hard to fix something if you don't know how it works ! Fixed ignition ? What did you fix or change ?
SERVICE THEFT SYSTEM
Security: Refer to Theft Systems Description and Operation in Theft Deterrent
You need to have it checked for trouble codes .
The theft deterrent system on this vehicle is comprised of two separate systems, the vehicle theft deterrent (VTD) system and the content theft deterrent (CTD) system. The VTD system prevents drive away theft by keeping the vehicle from starting. The CTD system is the vehicle alarm system which discourages unauthorized entry into the vehicle. These systems are described and diagnosed separately within this section.
Theft System Indicators
SECURITY The instrument panel cluster (IPC) illuminates the SECURITY indicator as determined by the vehicle theft deterrent (VTD) system and the content theft deterrent (CTD) system. The IPC receives a message from the theft deterrent control module or the rear integration module (RIM) via the serial data circuit requesting illumination.
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The VTD system requests the IPC to illuminate the indicator only when the ignition switch is ON. The VTD system uses the indicator as a malfunction indicator. For specific VTD condition that will illuminate the security indicator, refer to Vehicle Theft Deterrent (VTD) Description and Operation .

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The CTD system requests the IPC to illuminate the indicator only when the ignition switch is OFF. The CTD system uses the indicator in order to identify system status. For specific CTD condition that will illuminate the security indicator, refer to Content Theft Deterrent (CTD) Description and Operation .

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The IPC performs the displays test at the start of each ignition cycle. The indicator illuminates for approximately 3 seconds.
SERVICE THEFT SYSTEM The radio illuminates the SERVICE THEFT SYSTEM message when the VTD system detects a failure. The radio receives a message from the theft deterrent control module via the serial data circuit requesting illumination.
This is one you need to take to the dealer , unless you have a GM factory scan tool !

Most vehicles will reset the theft detterent system by locking and unlocking the doors with the key fob. Year/make/model??

It does it automaticly after car is locked ,so many seconds and the immobilisor is armed ,unless you have one of them weekend boy racer gizmos ,if you have then heaven help you when it packs up which it will ,what they called in america a viper or something .put the car in the garage and you will not have any problems and never leave anything in the car ,clear the junk out the garage first though its a garage for the car not a pool room or store room neither a granny annex .

did you try locking the car with the remote and also with the key. Alot of cars will disarm this way.