In this third paper of a series on the precision of obtaining ages of stellar populations using the full spectrum fitting technique, we examine the precision of this technique in deriving possible age spreads within a star cluster. We test how well an internal age spread can be resolved as a function of cluster age, population mass fraction, and signal-to-noise (S/N) ratio. For this test, the two ages (Age (SSP1) and Age (SSP2)) are free parameters along with the mass fraction of SSP1. We perform the analysis on 118,800 mock star clusters covering all ages in the range 6.8<log(age/yr)<10.2, with mass fractions from 10% to 90% for two age gaps (0.2dex and 0.5dex). Random noise is added to the model spectra to achieve S/N ratios between 50 to 100 per wavelength pixel. We find that the mean of the derived Age (SSP1) generally matches the real Age (SSP1) to within 0.1dex up to ages around log(age/yr)=9.5. The precision decreases for log(age/yr)>9.6 for any mass fraction or S/N, due to the similarity of SED shapes for those ages. In terms of the recovery of age spreads, we find that the derived age spreads are often larger than the real ones, especially for log(age/yr)<8.0 and high mass fractions of SSP1. Increasing the age gap in the mock clusters improves the derived parameters, but Age (SSP2) is still overestimated for the younger ages.