Spin-spin relaxation time ($T_2$) and magnetic susceptibility ($chi$) of the second layer $^3$He adsorbed on Grafoil, exfoliated graphite, preplated with a monolayer $^4$He are studied by pulsed-NMR in a density range of $0.68 leq rho leq 5.28$ nm$^{-2}$. The temperature dependence of $chi(T)$ and $chi(T = 0)$ show Fermi fluid behaviour and no evidence of self-condensation are found even at the lowest density $rho = 0.68$ nm$^{-2}$. Density dependence of $T_2$ at $f = 5.5$ MHz shows a broad maximum of 5.7 ms around $rho = 3$ nm$^{-2}$. Since the decrease of $T_2$ in dilute side can not be expected in the ideal 2D fluid, it can be understood as the relaxation caused by a small amount of solid $^3$He at heterogeneity of the substrate. We also measured the Larmor frequency dependence of $T_2$ at $rho = 5.28$ nm$^{-2}$. $1/T_2$ has a $f$-linear dependence similarly to the earlier study on a first layer solid $^3$He. From a comparison between our result and the earlier one, this linearity is almost independent of the particle motion. Now, it could be caused by a microscopic magnetic field inhomogeneity arisen from the mosaic angle spread and diamagnetism of the graphite substrate.
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