We demonstrate photoinduced spontaneous free-carrier generation in highly individualized (7,5)- chirality-enriched SWCNT samples ((7,5)-SWCNTs) suspended in a non-polar organic solvent. Frequency-resolved solution-phase flash photolysis time-resolved microwave conductivity (fp- TRMC), provides a contactless and quantitative measurement of the real and imaginary photoconductance of these individually suspended nanotubes. We use substantially lower excitation fluences than have been possible in previous studies, corresponding to absorbed photon densities of ~0.05 photons per micron length of (7,5)-SWCNTs, allowing us to avoid complications from dielectric screening by nearby excitons or exciton-exciton collisions. Even under these mild conditions, we unambiguously measure a photoconductance due to free carriers that are generated following excitation of both the first and second exciton transitions (S₁₁ and S₂₂, respectively). The low-fluence carrier generation quantum yield (Φ) with S₂₂ excitation appears c.a. 2.4 times higher than that with S₁₁ excitation, suggesting that the autoionization of S₂₂ excitons clearly enhances the carrier generation efficiency. In contrast, the transient decay dynamics are independent of excitation wavelength, suggesting that the mobile carriers generated from either S₁₁ or S₂₂ excitation undergo identical decay pathways (i.e. trapping, recombination, etc.).