The `<device-id>` is shown in the `xinput list` output - you can use the name as a string or the id number. You can query the actual button state using `xinput query-state <device-id>`.
The mouse has following button-ids:
| Button | ID |
|:----------------------|:--:|
| Thumb button | 9 |
| Index finger button | 1 |
| Middle finger button | 8 |
| Ring finger button | 3 |
| Wheel button | 2 |
| Wheel up | 4 |
| Wheel down | 5 |
See [remapping mouse buttons]({% post_url 2009-07-17-remapping-mouse-buttons %}) on what buttons X11 recognizes.
According to this the default configuration (`xinput set-button-map <device-id> 1 2 3 4 5 6 7 8 9`) would give you middle click on the wheel button and right-click on the middle finger.
The ring finger button would be for special use as well as the thumb button.
I for myself prefer having the middle-button on the middle finger and the right-click on the ring finger.
So I mapped 8→3 and 3→2 and I also mapped 9→8 and 2→9 to have the wheel button and thumb button for special use in some programs which make use of additional buttons.