Motivated by recent experimental progress, we study scalar wave propagation over an imperfect draining vortex, which can serve as an analog for rotating and nonrotating extreme compact objects (ECOs). We encapsulate the absorbing properties of the analog ECO by means of an effective boundary located around the analog horizon. The presence of reflection at the effective boundary, characterized by a single parameter K, allows for the existence of bound states located between the effective vortex core and the angular momentum barrier. The existence of these bound states leads to an enhanced absorption when the frequency of the incoming wave matches bound state frequencies, which result in Breit-Wigner type spectral lines in the absorption spectra. We also investigate the case of rotating analog ECOs. In this scenario, some of the bound states undergo superradiant amplification and become unstable. In both the rotating and nonrotating case, we calculate numerically transmission/reflection spectra exhibiting the enhanced absorption/amplification. We complement our numerical study with WKB estimates as well as an extension of the Pöschl-Teller toy model which we solve analytically. Our simple model exhibits distinctive properties which could be observed in future analog gravity experiments. We further argue that the observation of the spectral lines could be a way to characterize the effective field theory at play in the vicinity of the vortex core.