How do you hide the mouse pointer under Linux/X11?

Here's a description how unclutter utility does it.

Unclutter is a program which runs permanently in the background of an X11 session. It checks on the X11 pointer (cursor) position every few seconds, and when it finds it has not moved (and no buttons are pressed on the mouse, and the cursor is not in the root window) it creates a small sub-window as a child of the window the cursor is in. The new window installs a cursor of size 1x1 but a mask of all 0, ie an invisible cursor. This allows you to see all the text in an xterm or xedit, for example. The human factors crowd would agree it should make things less distracting.

Once created, the program waits for the pointer to leave the window and then destroys it, restoring the original situation. Button events are passed transparently through to the parent window. They will usually cause the cursor to reappear because an active grab will be made by the program while the button is down, so the pointer will apparently leave the window, even though its x y position doesnt change.

There is a -no-cursor option for Xorg 1.7 and later. https://www.x.org/wiki/AdvancedTopicsFAQ/

xinit -- -nocursor or startx -- -nocursor could work.

I'd rather use simpler method:

unclutter -idle 0

You almost do not see cursor, still it is available. To disable mouse:

rmmod psmouse

Or disable mouse module permanently somewhere in /etc/. See your distribution manual.