What are the scoping rules for options set on the background layer (with the backgrounds package)?

As illustrated by the pictures below, some options appear not to be constrained by their scope (e.g., line thickness and dashing) while others do. (Using the backgrounds package.) What is the rule? Separately, note the odd consequences for the arrowhead size.

documentclass{article}
usepackage{tikz}
usetikzlibrary{backgrounds}
begin{document}

begin{tikzpicture}[x=1in,y=1in]
draw[ultra thick,blue] (0,1) -- (2,1);
begin{scope}[on background layer]
draw (0,2) -- (2,0);
end{scope}
begin{scope}[on background layer={ultra thick,red,dashed,->,>=latex}]
draw (0,0) -- (2,2);
end{scope}
end{tikzpicture}
%
begin{tikzpicture}[x=1in,y=1in]
draw[ultra thick,blue] (0,1) -- (2,1);
begin{scope}[on background layer={red,dashed,ultra thick}]
draw (0,0) -- (2,2);
end{scope}
begin{scope}[on background layer={->,>=latex}]
draw (0,2) -- (2,0);
end{scope}
end{tikzpicture} 
end{document} 

documentclass{article}
usepackage{tikz}
usetikzlibrary{backgrounds}
begin{document}
    
    begin{tikzpicture}[x=1in,y=1in]
        draw[ultra thick,blue] (0,1) -- (2,1);
        begin{scope}[on background layer]
            draw (0,2) -- (2,0);
        end{scope}
        begin{scope}[on background layer={ultra thick,red,dashed,->,>=latex}]
            draw (0,0) -- (2,2);
        end{scope}
    end{tikzpicture}
    %
    begin{tikzpicture}[x=1in,y=1in]
        draw[ultra thick,blue] (0,1) -- (2,1);
        begin{scope}[on background layer={red,dashed,ultra thick}]
            draw (0,0) -- (2,2);
        end{scope}
        begin{scope}[on background layer={ultra thick,dashed,->,>=latex}]
            draw (0,2) -- (2,0);
        end{scope}
    end{tikzpicture} 
end{document}