Brie asked if I have a problem with students answering "yes" no matter what, as she has some students who would do just that!
I have those students, too, Brie! It's one of the reasons I started doing a question of the day in the first place. Some kiddos just default to "yes" (or "no," for that matter) for every question. To try to combat that, I always start with very concrete questions - such as "are you a boy?" "did you take the bus to school?" "are you wearing red?" etc. We can all call a student on an incorrect default answer if we all obviously know the answer they should give! I keep with the very concrete questions and explicitly choose questions those students have to answer "no" to, before moving onto more fun questions such as "do you like..." or "have you ever..." that staff may not actually know our students' answers to.
Peer pressure can also help here, to be honest. A girl who answers "yes" to "are you a boy" gets a chorus of "no, you're not!" from her classmates, we all have a (kind!) chuckle, and the student is invited to think about her answer and change it if needed!
You can also do an either/or question rather than yes/no, if that's easier for your students to answer - make a choice rather than answer explicitly. Sometimes I do this and then we label "Y" as the first choice and "N" as the second.
Another reader, Michie, asked about my system for Question of the Day (if I write students' names next to the answers on the chart, etc).
I don't write answers (but you definitely could!) but use velcroed name tags instead:
In the photo below, next to the switch, you can see our container of name tags we use for the Question of the Day poster. All staff members have a name tag, too (and there's a blank one for any visitors to our classroom), because we all answer the question! This way, staff can model appropriate answering, as well.
Michie also mentioned that she has some very low-functioning students who would not be physically able to hit a switch to answer. I have some of those students too.
If you have students who cannot yet answer a yes/no question in any way, I would stick with concrete questions you know the answers to, and assist them to answer until they are able to answer in some way themselves.
Also, in the absence of a two-button switch, I've often "labeled" (verbally) my hands in conversation with students. "Do you want _______, yes [wag left hand] or no [wag right hand]?" or, "Do you want option 1 [wag left hand] or option 2 [wag right hand]?" Students who do not have the fine motor function to hit a switch can often either look at the correct hand for an answer, or touch it (you can put your hands anywhere within their reach, further apart or closer together than a fixed switch, etc). This is also a great, versatile method of questioning if you find yourself without a usually-used switch or other communication method - like out in the community or in another room at school you've forgotten to bring along everything you need! I've made my students crack up before using this method for a four-option question by using my hands and feet, sitting on the floor and waving all four in the air at the mall as I wait for them to choose! "Should we go to the clothing store [left hand], the book store [left foot], the music store [right foot] or the food court [right hand]?" You do what it takes for communication!