  We have measured K-band surface brightness fluctuations (SBFs) of 19
early-type galaxies in the Fornax cluster. Combining our results with published
data, we find the absolute SBF magnitude Mbar_K = (-5.84)+(3.6)*[(V-I)-1.15].
The intrinsic cosmic scatter of Mbar_K appears to be larger than that of I-band
SBFs. The discovery of a correlation between K-band SBFs and V-I color is a new
clue into the star formation histories of early-type galaxies. This relation
naturally accounts for galaxies previously claimed to have anomalously bright
K-band SBFs, namely M32 and NGC 4489. Models indicate that the stellar
populations dominating the SBF signal have a significant range in age; some
scatter in metallicity may also be present. The youngest ages imply some
galaxies have very luminous giant branches, akin to those in intermediate-age
(few Gyr) Magellanic Cloud clusters. A few Fornax galaxies have unusually
bright K-band SBFs, perhaps originating from a high metallicity burst of star
formation in the last few Gyr. The increased spread and brightening of the
K-band SBFs with bluer (V-I) colors suggest that the lower mass cluster
galaxies may have had more extended and more heterogeneous star formation
histories than those of the more massive galaxies. (Abridged)
