TikZ Graph with usebox commands not working

This is an extended comment. When you say that something is "not working" you benefit a lot from indicating what the expected result is. The saveboxes behave no different from ordinary edge labels: if you place two identical ones in your setup, the second one will be swallowed.

documentclass{article}
usepackage{geometry}
usepackage{tikz}
usetikzlibrary{positioning,graphs}

begin{document}

%%% circuit breaker symbol, I will have other, more complicated usebox drawings in the final picture
%%% simple example shown for simplicity
newsavebox{tikzBRKt}
savebox{tikzBRKt}{%
    begin{tikzpicture}[ultra thick]
    draw (0,0) rectangle (1,1);
    end{tikzpicture}%
}
newcommand{tikzBRK}{usebox{tikzBRKt}}


begin{tikzpicture}[inner sep = 0pt, outer sep = 0pt,]
    tikzset{node distance = 1cm and 2cm}
coordinate (bjunc);
node (rbrk)     [right= of bjunc] {tikzBRK};
node (lbrk)     [left= of bjunc] {tikzBRK};
node (lbus)    [left=of lbrk] {};
node (rbus)    [right=of rbrk] {};
draw (lbrk) edge (bjunc) edge (rbrk)
      (lbus) edge (lbrk)
      (rbus) edge (rbrk);


begin{scope}[yshift=-2cm,local bounding box=A1]
  graph [grow right sep=2cm]{ lbus1/ -- "A" -- bjunc1/ -- "A" -- rbus1/ }; 
end{scope}
path (A1.west) node[left]{``not working''};

begin{scope}[yshift=-4cm,local bounding box=A2]
  graph [grow right sep=2cm]{ lbus1/ -- "A" -- bjunc1/ -- "B" -- rbus1/ }; 
end{scope}
path (A2.west) node[left]{``working''};


begin{scope}[yshift=-6cm,local bounding box=A3]
  graph [grow right sep=2cm]{ lbus1/ -- "tikzBRK" -- bjunc1/ -- "tikzBRK" -- rbus1/ }; 
end{scope}
path (A3.west) node[left]{``not working''};


begin{scope}[yshift=-8cm,local bounding box=A4]
  graph [grow right sep=2cm]{ lbus1/ -- "tikzBRK" -- bjunc1/ -- "{}tikzBRK" -- rbus1/ }; 
end{scope}
path (A4.west) node[left]{``working''};

end{tikzpicture}

end{document}

This is because, in your setting, the label also serves as an identifier. So the output of save boxes matches expectations.

By the same token, I do not understand your concerns regarding below=of lbus because there is no indication what the expected result is, and how the actual result differs from that.