To me it happens most often when the two languages are related: my Catalan interferes with my French, my French with my Catalan - German is not even in the room when I’m trying to speak one of those, but if I am trying to speak German, here comes English. Sometimes I’m speaking French, need to use a word that’s very similar in French and in English and mangle the pronunciation so it’s neither French nor English.
Related, I used to be somewhat conversational in American Sign Language, but I noticed it was dang near impossible to sign without moving my lips. What’s up with that?
When I studied German in 2008, I had previously dabbled in Esperanto for a bit. So often if I didn’t know the German word for something, the Esperanto word would pop into my head.
I get this with French and Russian - French being L3 and Russian L6. Somehow the German and the Czech that came in between are not affected so much, I’m not sure why, but those languages occupy different nodes in the brain for some reason. Even though my learning German sort of overlapped with my learning Russian (although at the time I was not formally in classes or studying in any way, just spending time in Germany and/or with Germans) German is rarely triggered when I speak Russian or vice versa. Czech and Russian do blend, but not in the sense that I’ll blurt out a word in one language while speaking the other, it’s more like I’ll make mistakes assuming that something that works in one language will work in the other, but it’s a more conscious process that reflects mistaken learning rather than some sort of cognitive overlap that will cause me to say things I know for a fact are not even wrong in a certain language, they’re not even in that language to begin with.
Habit.
Obviously, most of us associate communicating a thought with the lips and voice production. It actually is distracting to your listeners, who don know where to concentrate in space watching. And, as I mentioned above, it inhibits your signing by reinforcing your English thought mode, when you want to be at a place where you stick with the language you’re in.
Practice signing with water in your mouth.
I learned Hungarian in-country with my Peace Corps group and this happened to everyone. I think I had it worst because I’d throw in German words and I was usually dealing with Hungarians who also spoke German so the conversation would continue without them correcting me. It wasn’t until I started dating a woman who not only didn’t speak any German, she hated the sound of it and wouldn’t let me get away with it, that I finally stopped the habit.