I want to create the following template for the \tableofcontents in beamer.

I am able to generate the code for the list of sections and subsections with the following MWE
\documentclass{beamer}
\usepackage[english]{babel}
\usepackage{tikz}
\setbeamerfont{section in toc}{family*=qag, size=\large,series=\bfseries}
\setbeamerfont{subsection in toc}{size=\normalsize,series=\bfseries}
\setbeamertemplate{subsection in toc}{%
\begin{tikzpicture}[outer sep=0pt, inner sep=0pt,line width=0pt]
\path[use as bounding box] (0,0) rectangle (\textwidth,0);
\node[anchor=base east] at (.7\textwidth,0) { \inserttocsubsection};
\end{tikzpicture}
}
\setbeamertemplate{section in toc}{%
\begin{tikzpicture}[outer sep=0pt, inner sep=0pt,line width=0pt]
\path[use as bounding box] (0,0) rectangle (\textwidth,0);
\node[anchor=base east] at (.7\textwidth,0) { \inserttocsection};
\node[anchor=base west] at (.7\textwidth+4ex+2.2ex,0){\inserttocsectionnumber};
\end{tikzpicture}
}
\begin{document}
\begin{frame}
\tableofcontents
\end{frame}
\section{First Section}
\section{Second Section}
\subsection{A subsection}
\begin{frame}{Some frame}
\end{frame}
\end{document}
However, I do not find a smart way to insert the vertical line. If I use the background template, I can do it but the positioning is not easy (and strongly depends on the aspectratio and the margins). The same happens with overlay in tikzpicture. I tried to find a way to enclose the section in toc templates within a tikzpicture and define each template as a collection of nodes, but it seems \tableofcontets is more complex than I thought. For example, using \patchcmd is not a good choice.
