Customize bullet points in vertical timeline

Question

Based on Toggle bullet point in vertical timeline I want to customize the appearance of the bullet points in a tabular based setting. I want to use, e.g. \faArrowCircleLeft from fontawesome package. The glyph should appear above the vertical line. However, since the glyph is transparent, I wanted to put a circle in the background using tikz. I am not able to align the background accordingly, see the following example, where I used green color instead of white for the purpose of demonstration.

\documentclass{article}
\usepackage[dvipsnames]{xcolor}
\usepackage{etoolbox}
\usepackage{xtab}
\usepackage{array}
\usepackage{fontawesome5}
\usepackage{graphicx}
\usepackage{tikz}
\definecolor{accentcolor}{RGB}{ 250, 150, 10 }
\definecolor{accentcolortwo}{RGB}{ 50, 150, 10 }
\newbool{time_bullet}
\setbool{time_bullet}{true}
\renewcommand\arraystretch{2.8}
\newcommand{\foo}{\color{accentcolor!80}\vrule width 1pt 
    \makebox[0pt][c]{%
        \ifbool{time_bullet}{%
        \parbox{6pt}{\color{\accentcolor}{\tikz{
    \node[circle,fill=green,text width=0pt, xshift=-0pt, minimum width=0pt,inner sep=0pt, outer sep=0pt] {\faArrowCircleLeft} ;}
    }}\setbool{time_bullet}{false}}
{\setbool{time_bullet}{true}}
}\hskip-0.0pt\hspace{\labelsep}\ifbool{time_bullet}{\global\setbool{time_bullet}{false}}{\global\setbool{time_bullet}{true}}}
\newcolumntype{F}{<{\hskip 0pt} !{\foo} >{\raggedright\arraybackslash}p{3cm}}
\begin{document}
\begin{tabular}{lF}
     1 & Test\
    2 & Test \
    3 & Test
\end{tabular}
\end{document}

Answer 1

I rewrite the solution in LaTeX3, which supports stride values other than 2.

Update

\documentclass{article}
\usepackage[dvipsnames]{xcolor}
\usepackage{etoolbox}
\usepackage{xtab}
\usepackage{array}
\usepackage{fontawesome5}
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{adjustbox}
\usepackage{expl3}
\definecolor{accentcolor}{RGB}{ 250, 150, 10 }
\definecolor{accentcolortwo}{RGB}{ 50, 150, 10 }
\ExplSyntaxOn
\int_new:N \g_bullet_index_int
\dim_new:N \g_bullet_rule_width_dim
% vertical rule width
\dim_gset:Nn \g_bullet_rule_width_dim {1pt}
% bullet stride
\int_new:N \g_bullet_stride_int
% get the width of the arrow
\dim_new:N \g_arrow_width_dim
\hcoffin_set:Nn \l_tmpa_coffin {\faArrowCircleLeft}
\dim_gset:Nn \g_arrow_width_dim {\coffin_wd:N \l_tmpa_coffin}
% the value is used to compensate for bigger circle
% at the bottom
\fp_new:N \g_arrow_width_factor_fp
\fp_gset:Nn \g_arrow_width_factor_fp {0.90}
% compute new arrow width for background circle
\dim_new:N \g__arrow_width_dim
\dim_gset:Nn \g__arrow_width_dim {\fp_use:N\g_arrow_width_factor_fp \g_arrow_width_dim}
% compute lap value
\dim_new:N \g_bullet_lap_dim
\dim_gset:Nn \g_bullet_lap_dim {
  0.5\g_bullet_rule_width_dim + 0.5\g_arrow_width_dim
}
\newcommand*{\resetbullet}{
  \int_gset:Nn \g_bullet_index_int {0}
}
\newcommand*{\setbulletstride}[1]{
  \int_gset:Nn \g_bullet_stride_int {#1}
}
\newcommand{\dobullet}{
  % draw verticle rule
  \color{accentcolor!80}\vrule width \g_bullet_rule_width_dim
  % draw bullet at correct position
  \int_compare:nNnT { \int_mod:nn {\g_bullet_index_int} {\g_bullet_stride_int} } = {0} {
    \color{accentcolor}
    \adjustbox{left=0cm,
      lap=-\g_bullet_lap_dim}{
      \tikz{
        \node[circle, fill=accentcolor!80,
              minimum~width=\g_arrow_width_dim,
              inner~sep=0pt,
              outer~sep=0pt]
              {};
        \node[circle,fill=green,
              % manually tune the width of arrow so that their size fit
              minimum~width=\g__arrow_width_dim,
              inner~sep=0pt, 
              outer~sep=0pt] 
              {};
        \node[inner~sep=0pt,
              outer~sep=0pt]
              {\faArrowCircleLeft};
       }
     }
  }
  \hskip-0.0pt \hspace{\labelsep}
  % increment counter
  \int_gincr:N \g_bullet_index_int
}
\ExplSyntaxOff
\newcolumntype{F}{<{\hskip 0pt} !{\dobullet} >{\raggedright\arraybackslash}p{3cm}}
\begin{document}
\renewcommand\arraystretch{1.2}
% set stride to 2
\setbulletstride{2}
% reset bullet counter before new tabular
\resetbullet
\begin{tabular}{lF}
     1 & Test\
    2 & Test \
    3 & Test
\end{tabular}
\vspace{1em}
% set stride to 3
\setbulletstride{3}
% reset bullet counter before new tabular
\resetbullet
\begin{tabular}{lF}
     1 & Test\
    2 & Test \
    3 & Test \
    4 & Test
\end{tabular}
\end{document}