  We investigated the local magnetism of the organic conductor,
$\kappa$-(ET)$_{2}$Hg(SCN)$_{2}$Cl, with a quasi-triangular lattice of weakly
dimerized molecules through $^{13}$C NMR spectroscopy. The NMR spectra and
nuclear relaxation show that charge disproportionation occurs, associated with
the metal-insulator transition at 31 K. The relaxation rate indicates that the
paramagnetic spins in the insulating phase undergo a transition into a
spin-singlet ground state with the emergence of orphan spins, a possible
valence-bond-glass state. The present results are in high contrast to the
spin-cluster paramagnetism of the electric dipole-liquid candidate,
$\kappa$--(ET)$_{2}$Hg(SCN)$_{2}$Br, having nearly identical material
parameters. This fact indicates that these two systems are on the verge between
distinct phases in both charge and spin degrees of freedom; a spin-singlet
charge-ordered state versus a spin-active Mott insulating state, competing with
each other on a triangular lattice of dimerized sites.
