Entangled two-photon absorption (ETPA) hasrecently become a topic of lively debate, mainly due to theapparent inconsistencies in the experimentally reported ETPA crosssections of organic molecules obtained by a number of groups. Inthis work, we provide a thorough experimental study of ETPA inthe organic molecules Rhodamine B (RhB) and zinc tetraphenyl-porphirin (ZnTPP). Our contribution is 3-fold:first, we reproduceprevious results from other groups; second, we on the one handdetermine the effects of different temporal correlations introducedas a controllable temporal delay between the signal and idlerphotons to be absorbed on the strength of the ETPA signal, andon the other hand, we introduce two concurrent and equivalentdetection systems with and without the sample in place as a usefulexperimental check; third, we introduce, and apply to our data, a novel method to quantify the ETPA rate based on taking intoaccount the full photon-pair behavior rather than focusing on singles or coincidence counts independently. Through thisexperimental setup wefind that, surprisingly, the purported ETPA signal is not suppressed for a temporal delay much greater thanthe characteristic photon-pair temporal correlation time. While our results reproduce the previousfindings from other authors, ourfull analysis indicates that the signal observed is not actually due to ETPA but simply to linear losses. Interestingly, for higher RhBconcentrations, wefind a two-photon signal that, contrary to expectations, likewise does not correspond to ETPA