We employ low-temperature single-molecule spectroscopy combined with pattern recognition techniques for data analysis on a methyl-substituted ladder-type poly(para-phenylene) (MeLPPP) to investigate the electron-phonon coupling to low-energy vibrational modes as well as the origin of the strong spectral diffusion processes observed for this conjugated polymer. The results indicate weak electron-phonon coupling to low-frequency vibrations of the surrounding matrix of the chromophores, and that low-energy intrachain vibrations of the conjugated backbone do not couple to the electronic transitions of MeLPPP at low temperatures. Furthermore, these findings suggest that the main line-broadening mechanism of the zero-phonon lines of MeLPPP is fast, unresolved spectral diffusion, which arises from conformational fluctuations of the side groups attached to the MeLPPP backbone as well as of the surrounding host material.