Ah ok I see the issue. I assume you're connecting the button to the module through processor/parameter ID? The button only has two states, 0 and 1, so it will only change the Type parameter between those two values.
If you want it to cycle through more values you'll need to handle it through scripting by using a variable as a counter and increasing it each time the button is clicked, resetting when you get to the max (4) and passing the value to the EQ's Type attribute.
If your EQ has more than one band you'll need to use the band offset to select which band is affected by the button - forum search for "band offset".