Cognitive perspective-taking research has primarily been conducted under the rubric of theory of mind (ToM), with the core skill believed to involve the correct attribution of mental states to oneself and others as a means of explaining and predicting behavior. Relational frame theory (RFT) has provided a behavioral account of performances on true and false belief protocols by appealing to the three perspective-taking (deictic) relations. The current research sought to investigate the relative strength of cognitive perspective-taking abilities within the context of a false belief vignette and related IRAP. Experiment 1 investigated the impact of block order presentation and vignette stimuli order on IRAP performances. That is, across four conditions, rule order presentations (i.e., vignette consistent vs. vignette inconsistent) and vignette stimuli presentation were manipulated. Results indicated that vignette consistent responding was observed to varying degrees across conditions. To decrease this variability across conditions, Experiment 2 presented a vignette before each block of trials but again the IRAP showed only limited sensitivity to the vignette. The current findings and considerations for future research are discussed in terms of a recently published conceptual analysis of false belief by Kavanagh et al. (2020).