Unveiling the chemical fingerprints of the first (Population III, hereafter Pop III) stars is crucial for indirectly studying their properties and probing their massive nature. In particular, very massive Pop III stars explode as energetic pair-instability supernovae (PISNe), allowing their chemical products to escape in the diffuse medium around galaxies, opening the possibility to observe their fingerprints in distant gas clouds. Recently, three z > 6.3 absorbers with abundances consistent with an enrichment from PISNe have been observed with JWST. In this Letter, we present novel chemical diagnostics to uncover environments mainly imprinted by PISNe. Furthermore, we revise the JWST low-resolution measurements by analyzing the publicly available high-resolution X-Shooter spectra for two of these systems. Our results reconcile the chemical abundances of these absorbers with those from literature, which are found to be consistent with an enrichment dominated (>50% metals) by normal Pop II SNe. We show the power of our novel diagnostics in isolating environments uniquely enriched by PISNe from those mainly polluted by other Pop III and Pop II SNe. When the subsequent enrichment from Pop II SNe is included, however, we find that the abundances of PISN-dominated environments partially overlap with those predominantly enriched by other Pop III and Pop II SNe. We dub these areas confusion regions. Yet, the odd–even abundance ratios [Mg,Si/Al] are extremely effective in pinpointing PISN-dominated environments and allowed us to uncover, for the first time, an absorber consistent with a combined enrichment by a PISN and another Pop III SN for all the six measured elements.