Abstract: A recent study of gamma-ray data from the Galactic center motivates the investigation of light (similar to 7-10 GeV) particle dark matter models featuring tau-lepton pairs as dominant annihilation final state. The lepton-specific two-Higgs-doublet model provides a natural framework where light, singlet scalar dark matter can pair-annihilate dominantly into tau leptons. We calculate the nucleon-dark matter cross section for singlet scalar dark matter within the lepton-specific two-Higgs-doublet model framework, and compare with recent results from direct detection experiments. We study how direct dark matter searches can be used to constrain the dark matter interpretation of gamma-ray observations, for different dominant annihilation final states. We show that models exist with the correct thermal relic abundance that could fit the claimed gamma-ray excess from the Galactic center region and have direct detection cross sections of the order of what is needed to interpret recent anomalous events reported by direct detection experiments.