Hi,
The neutral safety switch will prevent the vehicle from starting but the switch will not prevent the vehicle from engaging any gears. The shifter cable is attached to the lever in your picture and this is attached to what is called the manual valve inside the transmission. When you move the position of this by the shifter the cable pulls the lever and manual valve which directs fluid inside the transmission to the appropriate gear.
If you don't have any movement, it could be low or no fluid pressure inside in the unit or the shifter may not be moving the lever on the outside of the transmission.
What you want to do is lift the drive wheels so the vehicle cannot move even if the transmission engages and then have someone shift the vehicle while you are watching this lever. If it is moving and sitting the correct detent then the manual valve is operating correctly. However, if it is not moving then your cable is the issue.
If it is moving then you have an issue inside the unit. More than likely the pump is failing. You can confirm this by measuring the pressure but this requires a special gauge or a scan tool.
Let me know what you find with the shifter and we can go from there. Thanks
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Saturday, August 3rd, 2019 AT 10:30 AM