I have been looking around for a formal (and easy to comprehend) definition of a general $n$-rank spinor. I have had no luck trying to find such a definition, or any definition for that matter.
So my question is; how would we in general define a $n$-rank spinor and given a 'thing' $\psi$ how could I test whether it was or was not a spinor?
An $n$-rank spinor in physics usually means a tensor product of $n$ left- and/or right-handed Weyl spinors. Equivalently, it is the total number of dotted and undotted indices on the spinor.
So e.g. in 3+1D, the irreducible representation $$(j_L,j_R), \qquad j_L, j_R~\in~ \frac{1}{2}\mathbb{N}_0,$$ [of the double cover $SL(2,\mathbb{C})$ for the restricted Lorentz group $SO^+(1,3;\mathbb{R})$] is a spinor of rank $n=2j_L+2j_R$. See also this Phys.SE post.
