Perspective-taking (PT) accessibility has been recognized as an important factor in affecting moral reasoning, also playing a non-trivial role in moral investigation towards autonomous vehicles (AVs). A new proposal to deepen this effect leverages the principles of the veil of ignorance (VOI), as a moral reasoning device aimed to control self-interested decisions by limiting the access to specific perspectives and to potentially biased information. Throughout two studies, we deepen the role of VOI reasoning in the moral perception of AVs, disclosing personal and contingent information progressively throughout the experiment. With the use of the moral trilemma paradigm, two different VOI conditions were operationalized, inspired by the Original Position theory by John Rawls and the Equiprobability Model by John Harsanyi. Evidence suggests a significant role of VOI reasoning in affecting moral reasoning, which seems not independent from the order in which information is revealed. Coherently, a detrimental effect of self-involvement on utilitarian behaviours was detected. These results highlight the importance of considering PT accessibility and self-involvement when investigating moral attitudes towards AVs, since it can help the intelligibility of general concerns and hesitations towards this new technology.