Speedometer and tachometer also the gear shift light not working

You are correct that this sounds like a vehicle speed sensor issue.

However, take a look at the wiring diagram below. This system has a buffer that is basically something that converts the speed signal and sends it to the cluster and PCM.

More than likely this buffer is failing when it gets hot, so we need to check the voltage on the dark green wire and see if this goes away when it gets hot.

Here is a guide that will help with this:

https://www.2carpros.com/articles/how-to-check-wiring

Basically, this circuit feeds the speedometer and then the PCM as well. The PCM then sends this message to the tach so if this wire is losing voltage, then that explains these issues.

Please let me know what you find with this.

Okay. Sounds good. Please let us know how it turns out.

Thanks for the update.

It could be and so we need to run through the testing that we will need to confirm this. It is a pretty simple circuit because the PCM just grounds the solenoid when it should be on so let's run through this testing and let me know what questions you have on this.

Thanks