Perhaps you can do something with polls, asking people how much more they would drive if gas were cheaper, how much less if it were more expensive. I've occasionally seen polls like that here and there; oddly, they only ever ask the second question, about gas getting more expensive. And people always say the same thing, they won't drive any less.

I don't know if I believe these polls, because they are asking people about hypotheticals and their actual responses might be different if the situations became real. They may also represent a certain stubbornness or defiance or even manipulativeness when people insist that they won't drive less.

I wonder if we would get more honest responses by asking if people would drive more if gas were cheaper. Suppose people are being manipulative, and trying to exaggerate the negative impact of higher prices, in order to rally political support for measures to keep prices low. Then they might similarly exaggerate the positive impact of lower prices, in order to gather support for measures to bring prices down. In that case they would claim to drive no less if prices rose, implying little elasticity, but to drive much more if prices fell, implying great elasticity. This would at least expose any such inconsistency and help us to evaluate the credibility of the answers, and also might give us a methodological tool: we could average the two results and perhaps get a better estimate of true elasticity of demand, giving insight into the shape of the demand curve.