The two-missing-elements perfect Skolem set conjecture

Let $A\subset\{1,2,\dots,n\}$ have cardinality $n-2$, with exactly two missing elements $a_i,a_j\in\{1,2,\dots,n\}$. The two-missing-elements perfect Skolem set conjecture. The set $A$ is a perfect Skolem set if and only if: (1) if $n\equiv0$ or $1$ modulo $n$, then $a_i\equiv a_j$ modulo $2$; (2) if $n\equiv2$ or $3$ modulo $n$, then $a_i\equiv a_j-1$ modulo $2$; and (3) $A\notin\{\{3\},\{2,4\},\{2,4,5\},\{3,4,5,6\}\}$. This is presented as a special case of the perfect Skolem set conjecture, with the listed exceptional sets accounting for failure of the density condition. The source gives no separate resolution status for this special case.