According to http://library.gnome.org/devel/vte/unstable/VteTerminal.html there's a "pointer-autohide" property which I'd very much like to be able to set. Quoting the vte documentation:
“Controls the value of the terminal's mouse autohide setting. When autohiding is enabled, the mouse cursor will be hidden when the user presses a key and shown when the user moves the mouse.”

Sounds like a candidate for the “advanced” tab in preferences.

Thanks for considering.