We prove necessary conditions for null-projected supersymmetric Yang--Mills theories with a Majorana--Weyl gaugino in signature $(s,t)$, under five explicit assumptions on the gaugino constraint, the transformation rules, the residual gauge field, the translation bracket and the absorption of the cubic gaugino terms. A real gaugino allows at most $\min(s,t)$ null vectors, the residual dimension must be two or ten, and $s-t$ must be $0$ or $\pm8$. The main step is a converse of the cubic gamma-matrix identity: if symmetric gamma matrices acting on $N$-component spinors in $d$ dimensions satisfy it, then $N=2(d-2)$. Consequently Nishino's construction does not transfer to the signatures $(11+8n)+3$ proposed by Rios, Marrani and Chester. In $27+3$ a real null frame has at most three vectors against Nishino's ten, the translation bracket allows only two, and with two the residual spinors have $4096$ components where absorption needs $48$. For unitary single-time theories with vanishing tensor charges on a massless multiplet, we also exclude every finite collection of scalar, spinor and vector polarizations when there are more than sixteen real supercharges. Theories outside the five assumptions are not decided.