I don't know that this is supported by any authority, but I feel that "persister" means "something that persists", whereas "persistor" means "something that provides persistence".
That said, I am a computer professional and this may just be in the realm of jargon.
If the answer (yes or no) is intentionally ambiguous, exploiting ambiguity describes the act of knowingly making such an answer to what is intended to be a multiple choice question. If the answer (yes or no) is unintentionally or inadvertently ambiguous, containing or involving ambiguity describes the act of unknowingly making such an answer.
To simplify those phrases to one word, a yes or no answer to a question intended to be a choice question (also called an alternative question), will always be ambiguous, and so the act of knowingly or unknowingly answering yes or no to a question intended to be a choice question may best be described as an ambiguous act.
Discarding the intentionality of the question's ambiguity (which I here distinguish from the ambiguity of the yes-no response), there are two types of ambiguity in the question: a 'polarity or alternativity' ambiguity, and an 'exclusive or inclusive disjunctivity' ambiguity.
Of the first type of ambiguity, polarity or alternativity, the question may be interpreted as asking for either polar (yes-no) or alternative (choice) answers. How the question is interpreted depends on the context. Usually, but not always, the likely interpretation will positively rule out one or the other of the types, yes-no or choice.
Of the second type of ambiguity, exclusive or inclusive disjunctivity, the question may be interpreted as containing either an exclusive or inclusive 'or'. If the 'or' is interpreted as being exclusive, the question will be interpreted as requiring a choice, that is, it will be considered a choice question and answered with one of "ice cream", "frozen yogurt", "neither", or "both". If the 'or' is interpreted as being inclusive, however, the question will be interpreted as being a polar (yes-no) question, and the answer will be "no" if neither of the two is liked, or "yes" if both are liked.
To sum up, your question here is not an easy question to answer unambiguously. If after reading this answer your interest in the subject persists, an article titled "Responding to alternative and polar questions" (by María Biezma and Kyle Rawlins, in Linguistics and Philosophy, October 2012, Volume 35, Issue 5, pp 361-406) examines the topic in some detail. Additionally, an article titled "On Polar Questions" (by Robert van Rooy and Marie Safarova) may give you entry into and perhaps suggest a path through the maze of ambiguity.
Best Answer
For the "multiple-choice", you could use "enumerated"; however, it probably makes more sense to just list the options, using a full phrase: "either
trueorfalse", "one of:json,xml,text", etc.For the "open-ended", you could use "free-form" or "arbitrary text"; but it's likely that there are some restrictions, in which case you can probably just describe those (e.g., "up to 128 characters", "cannot include whitespace") and leave it implied that there's not a fixed list of options.