I found the following information for the X1 Carbon User Guide, I hope it is helpful! I believe the Left Click button is what you are referring to when you said the Left thumb mouse button, close enough; I knew what you were referring to and that's all that really matters 
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5
Using the TrackPoint pointing device
The TrackPoint pointing device consists of a pointing stick 1 on the keyboard and three click buttons at the bottom of the keyboard. To move the pointer 5 on the screen, you apply pressure to the nonslip cap on the pointing stick in any direction parallel to the keyboard; the pointing stick itself does not move. The speed at which the pointer moves depends on the pressure you apply to the pointing stick. The functions of the left 4 and right 2 click buttons correspond to those of the left and right mouse buttons on a conventional mouse. The TrackPoint center button 3 called the scroll bar, enables you to scroll Web pages or documents in any direction with no need to use the graphic scroll bars on the side of the window.
Try custominzing the settings to see if makes a difference for the for clicking the Left click button.
You can customize the TrackPoint pointing device and its buttons as follows:
• Switch the functions of the left and right buttons.
• Change the sensitivity of the TrackPoint pointing device.
• Enable the Press-to-Select function.
• Enable the TrackPoint Scrolling Tips.
To customize the settings of the TrackPoint pointing device, do the following:
1. Go to Control Panel and click Hardware and Sound ➙ Mouse ➙ UltraNav.
2. Under TrackPoint, proceed to changing the settings.
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