When you use a foreign language IME from Google, how do you toggle languages?

[New Daddy]

When you use a foreign language IME from Google, how do you toggle languages form the sliding keyboard? In the portrait mode when you don't use Droid 4's sliding keyboard, the virtual keyboard displays a language button that can toggle languages. But in the landscape mode with the keyboard slid out, the virtual keyboard disappears and there seems to be no way to toggle between languages.

Any ideas?

 

[New Daddy]

When you use a foreign language IME from Google, how do you toggle languages form the sliding keyboard? In the portrait mode when you don't use Droid 4's sliding keyboard, the virtual keyboard displays a language button that can toggle languages. But in the landscape mode with the keyboard slid out, the virtual keyboard disappears and there seems to be no way to toggle between languages.

Any ideas?

I'm answering my own OP for the posterity's sake.
It turns out that there is a free, third-party app that does that. MultiLing Keyboard (https://play.google.com/store/apps/details?id=com.klye.ime.latin&hl=en) is very versatile and lets you fully take advantage of your external, sliding keyboard for those few who have them.