Solution-processed networks of semiconducting, single-walled carbon nanotubes (SWCNTs) have attracted considerable attention as materials for next-generation electronic devices and circuits. However, the impact of the SWCNT network composition on charge transport on a microscopic level remains an open and complex question. Here, we use charge-modulated absorption and photoluminescence spectroscopy to probe exclusively the mobile charge carriers in monochiral (6,5) and mixed SWCNT network field-effect transistors. Ground state bleaching and charge-induced trion absorption features, as well as exciton quenching are observed depending on applied voltage and modulation frequency. Through correlation of the modulated mobile carrier density and the optical response of the nanotubes, we find that charge transport in mixed SWCNT networks depends strongly on the diameter and thus bandgap of the individual species. Mobile charges are preferentially transported by small bandgap SWCNTs especially at low gate voltages, whereas large bandgap species only start to participate at higher carrier concentrations. Our results demonstrate the excellent suitability of modulation spectroscopy to investigate charge transport in nanotube network transistors and highlight the importance of SWCNT network composition for their performance.