Intermittent speedometer not working properly

This sounds like a possible cluster issue. The vehicle speed sensor sends a signal to the cluster where it displays the speed. However, let's start with checking for codes the next time the check engine light comes on. You can try and check for codes now but I am not sure they will be there.

Here is a guide that will help with this:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Let's start with this before we replace any parts because that could point us in a different direction.

Okay. I guess I misunderstood the idea that you can make the engine light go out by pressing on the cluster. I understood that to mean the light was on. If it is on then there should be codes.

As for the speedometer not working properly, that gets a direct signal from the vehicle speed sensor. Take a look at the wiring diagram. I highlighted the wire from the speed sensor to the speedometer.

If pressing on the cluster gets this to work, I can only imagine there is a circuit board issue with the cluster causing this issue.

If this does not address your question please provide more detail about what I am missing. Thanks