I have a 2 button trackball outputting the same code for left and right clicks.
The B: KEY bitmask appears to only enable one button:

I: Bus=0003 Vendor=068e Product=f700 Version=0111
N: Name="CH Products CH USB TRACKBALL"
P: Phys=usb-0000:00:14.0-6/input0
S: Sysfs=/devices/pci0000:00/0000:00:14.0/usb3/3-6/3-6:1.0/0003:068E:F700.0002/input/input6
U: Uniq=
H: Handlers=mouse1 event4
B: PROP=0
B: EV=17
B: KEY=10000 0 0 0 0
B: REL=3
B: MSC=10

Confirmed by the xorg log:

(II) config/udev: Adding input device CH Products CH USB TRACKBALL (/dev/input/event4)
() CH Products CH USB TRACKBALL: Applying InputClass "evdev pointer catchall"
(II) Using input driver 'evdev' for 'CH Products CH USB TRACKBALL'
(II) systemd-logind: got fd for /dev/input/event4 13:68 fd 28 paused 0
() CH Products CH USB TRACKBALL: always reports core events
() evdev: CH Products CH USB TRACKBALL: Device: "/dev/input/event4"
(--) evdev: CH Products CH USB TRACKBALL: Vendor 0x68e Product 0xf700
(--) evdev: CH Products CH USB TRACKBALL: Found 1 mouse buttons
(--) evdev: CH Products CH USB TRACKBALL: Found relative axes
(--) evdev: CH Products CH USB TRACKBALL: Found x and y relative axes
(II) evdev: CH Products CH USB TRACKBALL: Configuring as mouse
() evdev: CH Products CH USB TRACKBALL: YAxisMapping: buttons 4 and 5
() evdev: CH Products CH USB TRACKBALL: EmulateWheelButton: 4, EmulateWheelInertia: 10, EmulateWheelTimeout: >
() Option "config_info" "udev:/sys/devices/pci0000:00/0000:00:14.0/usb3/3-6/3-6:1.0/0003:068E:F700.0002/input>
(II) XINPUT: Adding extended input device "CH Products CH USB TRACKBALL" (type: MOUSE, id 10)
(II) evdev: CH Products CH USB TRACKBALL: initialized for relative axes.
() CH Products CH USB TRACKBALL: (accel) keeping acceleration scheme 1
() CH Products CH USB TRACKBALL: (accel) acceleration profile 0
() CH Products CH USB TRACKBALL: (accel) acceleration factor: 2.000
() CH Products CH USB TRACKBALL: (accel) acceleration threshold: 4
(II) config/udev: Adding input device CH Products CH USB TRACKBALL (/dev/input/mouse1)
(II) No input driver specified, ignoring this device.
(II) This device may have been added with another device file.

xinput shows a button left and a button unknown:

[root@localhost /]# xinput list-props 10
Device 'CH Products CH USB TRACKBALL':
Device Enabled (147): 1
Coordinate Transformation Matrix (149): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
Device Accel Profile (274): 0
Device Accel Constant Deceleration (275): 1.000000
Device Accel Adaptive Deceleration (276): 1.000000
Device Accel Velocity Scaling (277): 10.000000
Device Product ID (271): 1678, 63232
Device Node (270): "/dev/input/event4"
Evdev Axis Inversion (278): 0, 0
Evdev Axes Swap (280): 0
Axis Labels (281): "Rel X" (157), "Rel Y" (158)
Button Labels (282): "Button Left" (150), "Button Unknown" (272), "Button Unknown" (272), "Button Wheel Up" (153), "Button Wheel Down" (154)
Evdev Scrolling Distance (283): 0, 0, 0
Evdev Middle Button Emulation (284): 0
Evdev Middle Button Timeout (285): 50
Evdev Middle Button Button (286): 2
Evdev Third Button Emulation (287): 0
Evdev Third Button Emulation Timeout (288): 1000
Evdev Third Button Emulation Button (289): 3
Evdev Third Button Emulation Threshold (290): 20
Evdev Wheel Emulation (291): 0
Evdev Wheel Emulation Axes (292): 0, 0, 4, 5
Evdev Wheel Emulation Inertia (293): 10
Evdev Wheel Emulation Timeout (294): 200
Evdev Wheel Emulation Button (295): 4
Evdev Drag Lock Buttons (296): 0

I'm using more /etc/X11/xorg.conf.d/00-mouse.conf as

Section "InputDevice"
Identifier "Mouse0"
Driver "evdev"
# Option "Name" "CH Products CH USB TRACKBALL"
Option "Device" "/dev/input/mouse1"
Option "ZAxisMapping" "4 5 6 7"
Option "Emulate3Buttons" "yes"
EndSection

How would I enable the right button?

Why evdev, try libinput instead.

Hi Emerson, Thank you.

Unfortunately, I had the same result with libinput.