Understanding Wall's theorem on dependence of Lie relators in Burnside groups

G.E. Wall gave two different proofs of a remarkable result about the multilinear Lie relators satisfied by groups of prime power exponent $q$. He showed that if $q$ is a power of the prime $p$, and if $f$ is a multilinear Lie relator in $n$ variables where $n\neq1\operatorname{mod}(p-1)$, then $f=0$ is a consequence of multilinear Lie relators in fewer than $n$ variables. For years I have struggled to understand his proofs, and while I still have not the slightest clue about his first proof published in the Journal of Algebra, I finally have some understanding of his second proof published in a conference proceedings. In this note I offer my insights into Wall's second proof of this theorem.