Wanted to report back on some research and success enabling middle click action.
deepin doesn’t use libinput-gestures nor gesture-manager, although this is probably the correct answer on vanilla arch.
Deepin uses a built in touchpad solution controlled by dde-daemon. All touchpad gestures are controlled by the file /usr/share/dde-daemon/gesture.json. To enable middle click via 3-finger tap, add the following entry in the json array:
{
"Name": "tap",
"Direction": "none",
"Fingers": 3,