W530 middle button and right button indistinguishable

[cacophony]

I've been using a W520 for the past 6 years and just bought a W530.

I installed a fresh copy of Win 10. I did all the Windows updates, and then let the Lenovo site install/update drivers/etc. Part of this was the installation of the latest Synaptics Pointing Device Driver.

But when I use the middle button to scroll on my W530 it also brings up the context menu (the menu that typically shows up if you right click while in Chrome). Oddly this menu pops up when I release the middle button. To be clear, it does scroll properly and I even get the special scroll mode icon, but when I release the middle button it displays the context popup menu.

Looking further the right button has this same behavior. It's as if they're the same button.

I messed with the mouse settings, including the special trackpoint section but nothing I've tried has had any affect. I also tried installing the same (older) version of the Synaptics Pointing Device Driver that I saw I was using on my W520, but that made no difference.

Any idea what's going on here or how to fix this?

[RealBlackStuff]

Since the mouse buttons are part of it, bad keyboard?
Dirty KB-slot/connector?

[cacophony]

Thanks, that seems like a reasonable guess