Neutron capture cross sections are one of the fundamental nuclear data in the study of the s (slow) process of nucleosynthesis. More interestingly, the competition between the capture and the decay rates in some unstable nuclei determines the local isotopic abundance pattern. Since decay rates are often sensible to temperature and electron density, the study of the nuclear properties of these nuclei can provide valuable constraints to the physical magnitudes of the nucleosynthesis stellar environment. Here we report on the capture cross section measurement of two thallium isotopes, 204Tl and 205Tl performed by the time-of-flight technique at the n TOF facility at CERN. At some particular stellar s-process environments, the decay of both nuclei is strongly enhanced, and determines decisively the abundance of two s-only isotopes of lead, 204Pb and 205Pb. The latter, as a long-lived radioactive nucleus, has potential use as a chronometer of the last s-process events that contributed to final solar isotopic abundances.