Gnome-terminal doesn't have an option to disable hiding the mouse cursor. Moving the mouse will sometimes unhide it (not sure what the criterion is) and sometimes not. Many times you have to (as you have already noticed) actually click on the Window to unhide it. The problem with this is that if you have multiple terminal windows and multiple monitors, with the cursor hidden, you have no idea where you're clicking.
The resolution is to change the default terminal to a different emulator such as
xfece4-terminal or as mentioned in the comment
You'll also have to change the default terminal emulator to bring up your new configuration by default with:
$ gsettings set org.gnome.desktop.default-applications.terminal exec 'xfce4-terminal'
(Change xface4-terminal in the command to your alternate emulator.)