  Using the nucleon coalescence model based on kinetic freeze-out nucleons from
the 3D MUSIC+UrQMD and the 2D VISHNU hybrid model with a crossover equation of
state, we study the multiplicity dependence of deuteron ($d$) and triton ($t$)
production from central to peripheral Au+Au collisions at
$\sqrt{s_\mathrm{NN}}=$ 7.7, 14.5, 19.6, 27, 39, 62.4 and 200 GeV and Pb+Pb at
$\sqrt{s_\mathrm{NN}}=2.76$ TeV, respectively. It is found that the ratio $N_t
N_p/N_d^2$ of the proton yield $N_p$, deuteron yield $N_d$ and triton yield
$N_t$ exhibits a scaling behavior in its multiplicity dependence, i.e.,
decreasing monotonically with increasing charged-particle multiplicity. A
similar multiplicity scaling of this ratio is also found in the nucleon
coalescence calculation based on kinetic freeze-out nucleons from a multiphase
transport (AMPT) model. The scaling behavior of $N_t N_p/N_d^2$ can be
naturally explained by the interplay between the sizes of light nuclei and the
nucleon emission source. We further argue that the multiplicity scaling of $N_t
N_p/N_d^2$ can be used to validate the production mechanism of light nuclei,
and the collision energy dependence of this yield ratio can further serve as a
baseline in the search for the QCD critical point in relativistic heavy-ion
collisions.
