<p>This paper investigates the spectral form factor (SFF) of the quadratic <i>R</i>-para-particle Sachdev-Ye-Kitaev (<i>R</i>-PSYK₂) model with various random matrix ensemble couplings. We generalize previous work on Gaussian Unitary Ensemble (GUE) couplings to all three Gaussian ensembles (GUE, GOE, GSE) and three circular ensembles (CUE, COE, CSE). Through analytical and numerical methods, we establish precise correspondences between GUE and CUE results, demonstrating their SFFs satisfy <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">K</mi> <mi>GUE</mi> </msub> <mfenced close=")" open="("> <mrow> <mn>2</mn> <mi>t</mi> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{K}}_{\textrm{GUE}}(2t) \)</EquationSource> </InlineEquation> ≈ <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">K</mi> <mi>CUE</mi> </msub> <mfenced close=")" open="("> <mi>t</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{K}}_{\textrm{CUE}}(t) \)</EquationSource> </InlineEquation> in the time regime 1 ≪ <i>t</i> ≪ <i>N</i>. For the symplectic ensembles, we observe similar behavior with appropriate time rescaling, while we only provide the calculation method for the orthogonal ensembles.</p>