  The $p_T$ dependent elliptic and triangular flow parameters of direct photons
are known to be dominated by thermal radiations. The non-thermal contributions
dilute the photon anisotropic flow by adding extra weight factor in the $v_n$
calculation. The discrepancy between experimental photon anisotropic flow data
and results from theoretical model calculations is not well understood even
after significant developments in the model calculations as well as in the
experimental analysis. We show that the ratio of photon $v_n$ can be a
potential observable in this regard by minimizing the uncertainties arising due
to the non-thermal contributions. We calculate the $v_2/v_3$ of photons as a
function of $p_T$ from heavy ion collisions at RHIC and compare the results
with available experimental data. The ratio does not change significantly $p_T$
in the region $p_T>2$ GeV. However, it rises towards smaller $p_T$ ($< 2$ GeV)
values. The ratio is found to be larger for peripheral collisions than for
central collisions. In addition, it is found to be sensitive to the initial
formation time and the final freeze-out temperature at different $p_T$ regions
unlike the individual anisotropic flow parameters. We show that the photon
$v_1/v_2$ and $v_1/v_3$ along with the $v_2/v_3$ results may help us
constraining the initial conditions.
