Troubleshooting Overdrive Disengagement

Finally decided to try and track down the cause of my overdrive not kicking on/off when I hit the button on the auto shifter and need some guidance. When I am driving and go to hit the button to turn it off while climbing a grade, I don’t get any dash lights, no 3rd gear hold, just the satisfaction of clicking a button.

I am testing the button itself with my multimeter on the lowest ohm setting (200) and am getting a 1 on the screen until I press the button. It drops to zero as long as i’m holding the button, then when I let go it pops back to 1. I think my switch is faulty based off this, but I fucking suck at electrical diagnostics so looking for some input here.

If my switch is working properly, would I check the solenoid next?

Here’s how I’m testing the button, starts at 1, falls to zero as long as it’s pressed, then back to 1.