Firefox Tab Switching

Firefox won’t tab-switch out of Gmail/Compose

I constantly use Ctrl-PageUp and Ctrl-PageDown to switch from one Firefox tab to another.

However, when I open a new outgoing message in Gmail, Ctrl-PageUp and Ctrl-PageDown don’t work. I can switch with a mouse click, but I want my keyboard shortcut.

Is there a setting I can change on Firefox’s about:config page, or perhaps in Gmail to make it let go of the focus?