Custom click button 3?

I have an Evoluent mouse that I am trying to remap the mouse buttons. The mouse has Left click, Middle click, Right click, and Buttons 3, 4, and 5.

I want to swap buttons 3, 4, and 5 such that 3 -> 4, 4 -> 5, and 5 -> 3. I can do the first two, but in the Custom Click configuration there is no Button 3 that I can select.

Is the option for Button 3 missing, or am I misunderstanding how the mouse buttons work?

Thanks

Button 3 is the middle click button

Thanks for the reply!

That's what I thought initially too, I was surprised that there is a separate Button 3. But the UI is showing them as separate buttons. Here are the screenshots:


For reference the mouse I am using is this: https://www.amazon.com/Evoluent-VM4R-VerticalMouse-Ergonomic-Connection/dp/B00427TAIK/ref=pd_lpo_2?pd_rd_i=B00427TAIK&psc=1

And the detected buttons are shown in these pictures:


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I'm having the same issue. Button 3 is NOT (commonly) middle mouse click. As maurice points out, if I click the "back/bottom arrow" button on my Corsair mouse in BTT's "Record a mouse button" tray, it returns button 3!