Poking around for a bit I found that the left mouse button is the [5] key on the numpad, and the right mouse button is the context menu key (which you also find on the mute key using [FN]).
For those that have frequent problems with the built-in mouse buttons and find that the accessibility options used to map them are unreliable, here's a simple solution: https://github.com/AyrA/MouseRemap
This repository contains an autohotkey script to remap the fake buttons to real mouse buttons. A readme is provided with details and instructions, but it's fairly trivial to use.
Don't forget to disable the keyboard mouse in the accessibility settings if you want to use this.
works great