Passkey bypass?

The resistor bypass only worked on the Passkey I VATS that have a resistance pellet in the key itself. The last vehicle built with it was in 2003. The Passlock VATS that your car uses has a magnet on the lock cylinder that rotates and activates a hall effect circuit that sends a signal to the ECU through the security module that tells it you have the correct key. That signal however isn't a simple resistance, instead the hall effect works like a switch and the circuit generates a specific frequency based on the resonator circuit in the hall effect. The programming steps let the system learn what "note" the sensor in your hall effect device "sings" at. When it sees that "note" on the wires it says the proper key is in use and starts the engine. However, that signal isn't always on, it is only active in the start position of the key, then in run it shuts off. The only resistor is a 1.3K that acts to lower current through the sensor. They system basically works like this - Key goes into lock, that triggers the key in lock switch that causes the chimes if the door is open and tells the ECU that there is a key. You turn the key to start and as it passes the ON/RUN position it simply wakes up the other parts of the VATS. Once you get to the START position the magnet triggers the hall effect and the signal goes through the system to the antitheft system, which confirms the signal is correct and the ECU can activate the fuel system so the engine can start. You release the key back to the ON/RUN position and the signal from the hall effect stops. This tells the security system that it is a valid key and not a false signal and the engine continues to run.
This system though has a lot more failures than the earlier system. One of the most common is for the hall effect module to fail. They can fail on or off but the result is the same, the engine will start, run a few seconds then shut off.
There are companies that sell "bypass modules" but the catch is that most don't work properly because of the way the factory system turns the signal on/off with the magnet. It isn't just the signal frequency that counts but also the time between the magnet turning the HES on and when it returns to run the amount of time between the magnetic field turning off the sensor and the switch moving into the run position. That can change depending on the sensors construction and the strength of the magnet.
Now all of that said there really isn't a simple resistor bypass with them. Instead you replace the part of the system that failed. The toggle only triggers the prime circuit which turns the pump on for 3 seconds to fill the lines, then it turns the starter which starts the engine. Without the signal from the immobilizer the pump stays off and the engine shuts off as soon as that initial prime pressure is gone.
The easiest way to repair them is to replace the ignition lock cylinder housing. If you have a working key this is much easier as you won't end up with multiple keys. You would get the new lock housing, remove your existing one, use the key to release the current ignition cylinder and remove it, then swap it into the new housing. Install the new housing, do the relearn and you would be done.
I generally recommend getting a new switch from GM, there are some aftermarket ones out there but most are very poor quality electrically. You can use a used one but it's harder to program them.
Replacing the switch itself isn't difficult it's just time. You remove the knee bolster trim under the dash, then the instrument cluster and you can get to the three bolts that hold the switch in place. Disconnect the electrical connector and remove the 3 bolts. Remove the switch.
Now with a working key, insert the key into the lock, turn it to ON/RUN and push the release tab. Remove the lock cylinder. Now repeat that process on the other cylinder. If you get a used switch with no key you can take it to a locksmith and they can remove the cylinder without damaging the housing. Now you install your cylinder in the replacement switch and bolt that switch in and connect it.
Now as for the relearn process, it's a pain, you have to use a scan tool. That is because you need to do a data transfer between the old module and the replacement so the theft system recognizes the replacement. If you have a factory level tool it will have the directions to follow in the security system menus. You would run the 10 minute procedure and then follow the scan tool. You are replacing the TDM so you will note steps that warn you about the fuel control password requiring the scan tool to program it, that is the part that keeps the engine from running, if you don't do it the replacement will end up with the vehicle in the same condition it is now. It's also why I generally tell people to let a dealer or qualified shop to do this repair, it is really easy to go out of order and not solve the problem.

10-Minute Relearn Procedure

When performing the 10-minute relearn procedure, all previously learned keys will be erased from the TDM memory. Additional keys may be learned after performing the relearn procedure.

Use only a master key when performing the first relearn procedure. If you a valet key is used first, the TDM will not allow additional keys to be learned.

Use this procedure after replacing any of the following components:

* The vehicle keys
* The TDM
* The engine control module (ECM)

1. When replacing either the vehicle keys, PCM, or TDM and the 10-Minute Relearn Procedure is used, ensure that the appropriate calibration is selected for the replacement component on the calibration selection screen of the service programming system. The appropriate calibrations for specific vehicle theft deterrent (VTD) system components are described below.

When preparing a TDM for replacement, the Prepare Module For TDM Setup Procedure calibration is required. This allows the retrieval of required information from the TDM prior to its replacement.

When learning vehicle keys and the 10-Minute Relearn Procedure is used, the Vehicle Theft Deterrent Learn For Learning Replacement Keys calibration is required. This clears all previously learned keys from the TDM and enables the TDM to learn new vehicle keys. For learning additional vehicle keys, refer to Adding Keys.

When replacing a TDM or ECM and the 10-Minute Relearn Procedure is used, the VTD Learn for Powertrain calibration is required. This clears the previously learned fuel continue password in the ECM and enables the ECM to learn the fuel continue password of the new TDM.

Important: When replacing a TDM with a GM SPO replacement part, ensure the Setup a New TDM procedure is performed prior to the 10-Minute Relearn Procedure.

Connect a scan tool to the vehicle.

2. Turn ON the ignition, with the engine OFF.
3. Ensure that all power consuming devices are turned OFF on the vehicle.
4. With a scan tool, select Request Info. Under Service Programming System and follow the scan tool on-screen instructions.
5. Disconnect the scan tool from the vehicle and connect the scan tool to a Techline Terminal with the current Service Programming System (SPS) software.
6. On the Techline Terminal, select Service Programming System and follow the Techline Terminal on-screen instructions. Ensure the correct programming procedure is selected based on the component being replaced or programmed. See Important above.
7. Disconnect the scan tool from the Techline Terminal and re-connect the scan tool to the vehicle.
8. With a master vehicle key, turn ON the ignition, with the engine OFF.
9. With a scan tool, select Program ECU under Service Programming System.
10. At this point the scan tool must remain connected for the duration of the 10-Minute Relearn Procedure.

The scan tool will initially display 12 Minutes. The first 2 minutes allow the scan tool to initialize the appropriate control module. The remaining 10 minutes is the relearn timer.

On some vehicles the security indicator may be illuminated on steady for the duration of the 10-Minute Relearn Procedure.

Observe the scan tool. After approximately 10 minutes, the scan tool will display Programming Successful, Turn OFF Ignition. The vehicle is now ready to relearn the key information and/or the passwords on the next ignition switch transition from OFF to CRANK.

11. Turn OFF the ignition and wait 5 seconds.
12. With a master vehicle key, start the vehicle. The TDM has now learned the key transponder information and/or the ECM has now learned the fuel continue password.
13. If additional keys are required to be learned, refer to Adding Keys.
14. With a scan tool, clear any DTCs.