Galaxies often contain large reservoirs of molecular gas which shape their evolution. This can be through cooling of the gas -- which leads to star formation, or accretion onto the central supermassive black hole -- which fuels AGN activity and produces powerful feedback. Molecular gas has been detected in early-type galaxies on scales of just a few tens to hundreds of solar masses by searching for absorption against their compact radio cores. Using this technique, ALMA has found absorption in several brightest cluster galaxies, some of which show molecular gas moving towards their galaxy's core at hundreds of km/s. In this paper we constrain the location of this absorbing gas by comparing each galaxy's molecular emission and absorption. In four galaxies, the absorption properties are consistent with chance alignments between the continuum and a fraction of the molecular clouds visible in emission. In four others, the properties of the absorption are inconsistent with this scenario. In these systems the absorption is likely produced by a separate population of molecular clouds in close proximity to the galaxy core and with high inward velocities and velocity dispersions. We thus deduce the existence of two types of absorber, caused by chance alignments between the radio core and: (i) a fraction of the molecular clouds visible in emission, and (ii) molecular clouds close to the AGN, in the process of accretion. We also present the first ALMA observations of molecular emission in S555, Abell 2390, RXC J1350.3+0940 and RXC J1603.6+1553 -- with the latter three having molecular masses of $>10^{10}$M$_{\odot}$.