Structures of the [C₆H₆-(CH₃OH)₂]⁺ cluster cation are investigated with infrared (IR) spectroscopy. While the noncovalent type structure has been confirmed for the n = 1 cluster of [C₆H₆-(CH₃OH)_n]⁺, only contradictory interpretations have been given for the spectra of n = 2, in which significant changes have been observed with the Ar tagging. In the present study, we revisit IR spectroscopy of the n = 2 cluster from the viewpoint of the σ-complex structure, which includes a covalent bond formation between the benzene and methanol moieties. The observed spectral range is extended to the lower-frequency region, and the spectrum is measured with and without Ar and N₂ tagging. A strongly hydrogen-bonded OH stretch band, which is characteristic to the σ-complex structure, is newly found with the tagging. The remarkable spectral changes with the tagging are interpreted by the competition between the σ-complex and noncovalent complex structures in the [C₆H₆-(CH₃OH)₂]⁺ system. This result shows that the microsolvation only with one methanol molecule can induce the σ-complex structure formation.