Infrared messenger-tagging predissociation action spectroscopy (IRPD) is a well-established technique to record vibrational spectra of reactive molecular ions. One of its major drawbacks is that the spectrum of the messenger-ion complex is taken instead of that of the bare ion. In particular for small open-shell species, such as the Renner-Teller (RT) affected HCCH+ and DCCD+, the attachment of the tag may have a significant impact on the spectral features. Here we present the application of the novel leak-out spectroscopy (LOS) as a tag-free method to record the cis-bending of the HCCH+ (∼700 cm-1) and DCCD+ cations (∼520 cm-1), using a cryogenic ion trap end user station at the FELIX laboratory. We demonstrate that the obtained LOS spectrum is equivalent to a previously recorded laser-induced reactions (LIR) spectrum of HCCH+. The bending modes are the energetically lowest-lying vibrational modes targeted with LOS so far, showing its potential as a universal broadband spectroscopic technique. Furthermore, we have investigated the effect of the rare gas attachment by recording the vibrational spectra of Ne- and Ar-tagged HCCH+. We found that the Ne-attachment led to a shift in band positions and change in relative intensities, while the Ar-attachment even led to a complete quenching of the RT splitting, showing the importance of using a tag-free method for RT affected systems. The results are interpreted with the help of high-level ab initio calculations in combination with an effective Hamiltonian approach.