Optical studies of the density wave (DW) salt of α-(BEDT-TTF) 2 KHg(SCN) 4 revealed a pseudogap due to a charge fluctuation below T * 200 K. Moreover, 13 C-NMR studies of the DW salt of α-(BEDT-TTF) 2 RbHg(SCN) 4 and of the superconductivity (SC) salt of α-(BEDT-TTF) 2 NH 4 Hg(SCN) 4 suggested that the NMR line width of the A site increased and the charge disproportionation in the A column developed below T *. These phenomena may be due to the development of a horizontal stripe modulation of the local charge density. However, whether the horizontal stripe modulation develops or not and the relationships among T * anomalies, the pseudogap, and line broadening, were unclear. In this study, 13 C-NMR measurements were obtained of the metallic salt of α-(BEDT-TTF) 2 TlHg(SeCN) 4 , and its electronic structure was compared with those of the DW and SC salts. The NMR line width of the A site and χ B /χ C in Rb(SCN) and NH 4 (SCN) increased and deviated from that in Tl(SeCN) below T * , suggesting the development of the instability of horizontal stripe modulation in Rb(SCN) and NH 4 (SCN) and that T * anomalies could be due to the instability.