OK so it turns out I lied.  It doesn't always work on Antergos either. It seems to happen randomly and how to get it working again is also a mystery.  Resetting BIOS default does not restore it, and neither does booting into Windows - where it's not working there either. I unplugged both the power cable and the USB mouse then just kept restarting it until it mysteriously started working again.
Attached is the full dmesg logs for both working (YES) and not (NO). Here the pertinent parts:

// NOT WORKING //
$ grep -i hid EZBook*
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    0.000000] Command line: \\boot\vmlinuz-linux ro root=UUID=db197dac-84a9-48f2-8de2-803e79eb2a95 initrd=boot\initramfs-linux.img i2c-hid.dyndbg=+p
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    0.000000] Kernel command line: \\boot\vmlinuz-linux ro root=UUID=db197dac-84a9-48f2-8de2-803e79eb2a95 initrd=boot\initramfs-linux.img i2c-hid.dyndbg=+p
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    1.796661] hidraw: raw HID events driver (C) Jiri Kosina
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    1.800642] usbcore: registered new interface driver usbhid
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    1.800644] usbhid: USB HID core driver
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    1.802083] hid-generic 0003:275D:0BA6.0001: input,hidraw0: USB HID v1.11 Mouse [USB OPTICAL MOUSE ] on usb-0000:00:15.0-2/input0
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    8.334410] input: Intel HID events as /devices/platform/INT33D5:00/input/input3
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    8.334430] intel-hid INT33D5:00: platform supports 5 button array
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    8.334475] input: Intel HID 5 button array as /devices/platform/INT33D5:00/input/input4
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[    8.471540] i2c_hid i2c-SYNA3602:00: Requesting IRQ: 154
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   13.490316] i2c_hid i2c-SYNA3602:00: failed to reset device.
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   14.507051] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   14.514231] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   19.676987] i2c_hid i2c-SYNA3602:00: failed to reset device.
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   25.863656] i2c_hid i2c-SYNA3602:00: failed to reset device.
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   26.880415] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   26.888099] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   32.050315] i2c_hid i2c-SYNA3602:00: failed to reset device.
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   33.063375] i2c_hid i2c-SYNA3602:00: can't add hid device: -61
EZBook3Pro-touchpad-NO.Antergos.dmesg.txt:[   33.069267] i2c_hid: probe of i2c-SYNA3602:00 failed with error -61

// WORKING //
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    0.000000] Command line: \\boot\vmlinuz-linux ro root=UUID=db197dac-84a9-48f2-8de2-803e79eb2a95 initrd=boot\initramfs-linux.img i2c-hid.dyndbg=+p
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    0.000000] Kernel command line: \\boot\vmlinuz-linux ro root=UUID=db197dac-84a9-48f2-8de2-803e79eb2a95 initrd=boot\initramfs-linux.img i2c-hid.dyndbg=+p
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    8.337982] input: Intel HID events as /devices/platform/INT33D5:00/input/input2
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    8.338004] intel-hid INT33D5:00: platform supports 5 button array
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    8.338054] input: Intel HID 5 button array as /devices/platform/INT33D5:00/input/input3
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    8.389727] hidraw: raw HID events driver (C) Jiri Kosina
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[    8.448980] i2c_hid i2c-SYNA3602:00: Requesting IRQ: 154
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[   13.490334] i2c_hid i2c-SYNA3602:00: failed to reset device.
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[   14.507090] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[   14.514337] i2c_hid i2c-SYNA3602:00: i2c_hid_get_input: incomplete report (27/34)
EZBook3Pro-touchpad-YES.Antergos.dmesg.txt:[   14.899654] hid-multitouch 0018:0911:5288.0001: input,hidraw0: I2C HID v1.00 Mouse [SYNA3602:00 0911:5288] on i2c-SYNA3602:00