There is actually a really good primer on questionnaire design on coursera: https://www.coursera.org/learn/questionnaire-design
It is taught by some very prominent figures in survey research and I really enjoyed watching their videos.
In terms of techniques, I can think of two main ones as it relates to survey methodology and questionnaire design.
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You preface the question with a qualifier to make the behavior seem more acceptable and less taboo, e.g., "Some people own guns in the US for hunting, collecting or self-defense...", or you can preface with a reminder "As a reminder, you identity is protected and none of your responses will be tied to you in any way..."
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A more novel technique and one that I haven't actually seen in practice, is a second stage of randomization at the question level. You ask the participant to flip a coin, and say "If it is heads, please answer the question, 'Do you own a gun, yes or no?' and if it is tails,'Do you own a pet, yes or no?'". From there you can back out the probability of a respondent answering both questions and get an accurate estimate of gun ownership without ever knowing if any individual participant actually answered the gun question.
In terms of trends, assuming reluctance to self identifying as a gun owner is a constant over time, you can reasonable assume that a change you see in your estimate is a real change in gun ownership.
There are actual proxies from administrative data but I don't deal with them as much as I work mostly in primary data collection.