What do you think of this design?

    -- run within https://akkartik.itch.io/carousel
    g = love.graphics
    rect = g.rectangle
    color = g.setColor
    floor = math.floor

    Limit = 13
    Byo_yomi_period = 30  -- seconds

    Curr_color = 'black'
    Byo_yomi = {
      black=0,
      white=0,
    }

    Curr_time = 0

    function car.update(dt)
      if Byo_yomi.black == Limit or Byo_yomi.white == Limit then
        return
      end
      Curr_time = Curr_time + dt
      if Curr_time > Byo_yomi_period then
        Byo_yomi[Curr_color] = Byo_yomi[Curr_color] + 1
        Curr_time = Curr_time - Byo_yomi_period
      end end

    -- initialize space per side
    local side_w = floor((Safe_width-60 - 100)/2)

    -- initialize font size
    local function font_size_for_chess_clock()
      local font_size
      local min_font_size = 20
      local max_font_size = Safe_height
      for i=1,100 do
        if min_font_size >= max_font_size-5 then
          break
        end
        font_size = floor((min_font_size+max_font_size)/2)
        local font = g.newFont(font_size)
        local w = font:getWidth('00:00:00')
        if w < side_w then
          min_font_size = font_size
        elseif w > side_w then
          max_font_size = font_size
        elseif w == side_w then
          break
        end
      end
      return font_size
    end

    local large_font_size = font_size_for_chess_clock()
    local large_font = g.newFont(large_font_size)
    local small_font_size = 20
    local small_font = g.newFont(small_font_size)

    function car.draw()
      local top = Menu_height+20
      local x = 30
      local height = Safe_height-80
      local gutter_width = 100
      -- black side
      color(0.2,0.2,0.2)
      rect('fill', x, top, side_w, height, 5,5)
      color(1,1,1)
      local y
      if Byo_yomi.black < Limit - 10 then
        y = top + (height-large_font_size)/2
        print_centered(large_font, Byo_yomi.black, y, x, side_w)
        if Curr_color == 'black' then
          y = y + large_font_size + 10
          print_centered(small_font, floor(Curr_time), y, x, side_w)
        end
      elseif Byo_yomi.black < Limit-1 then
        y = top + (height - large_font_size*2 - 10)/2
        local s = ('%d left'):format(Limit - Byo_yomi.black)
        print_centered(large_font, s, y, x, side_w)
        if Curr_color == 'black' then
          y = y + large_font_size + 10
          print_centered(large_font, floor(Curr_time), y, x, side_w)
        end
      elseif Byo_yomi.black == Limit-1 then
        y = top + (height - large_font_size - 10 - small_font_size)/2
        print_centered(small_font, "no time left", y, x, side_w)
        if Curr_color == 'black' then
          y = y + small_font_size + 10
          print_centered(large_font, floor(Curr_time), y, x, side_w)
        end
      else
        -- out of time; Byo_yomi.black == Limit
        -- print nothing
      end
      -- white side
      x = x + side_w + gutter_width
      color(0,0,0)
      rect('line', x, top, side_w, height, 5,5)
      if Byo_yomi.white < Limit-10 then
        y = top + (height-large_font_size)/2
        print_centered(large_font, Byo_yomi.white, y, x, side_w)
        if Curr_color == 'white' then
          y = y + large_font_size + 10
          print_centered(small_font, floor(Curr_time), y, x, side_w)
        end
      elseif Byo_yomi.white < Limit-1 then
        y = top + (height - large_font_size*2 - 10)/2
        local s = ('%d left'):format(Limit - Byo_yomi.white)
        print_centered(large_font, s, y, x, side_w)
        if Curr_color == 'white' then
          y = y + large_font_size + 10
          print_centered(large_font, floor(Curr_time), y, x, side_w)
        end
      elseif Byo_yomi.white == Limit-1 then
        y = top + (height - large_font_size - 10 - small_font_size)/2
        print_centered(small_font, "no time left", y, x, side_w)
        if Curr_color == 'white' then
          y = y + small_font_size + 10
          print_centered(large_font, floor(Curr_time), y, x, side_w)
        end
      else
        -- out of time; Byo_yomi.white == Limit
        -- print nothing
      end end

    function print_centered(font, msg, y, left, width)
      local w = font:getWidth(msg)
      local x = left + (width-w)/2
      g.setFont(font)
      g.print(msg, x,y)
    end

    function car.mouse_press(x,y, b)
      if Byo_yomi.black == Limit or Byo_yomi.white == Limit then
        return
      end
      if y >= Menu_height + 20 then
        if Curr_color == 'black' then
          -- it's black's move
          if x <= 30+side_w then
            Curr_color = 'white'
            Curr_time = 0
          end
        else
          -- it's white's move
          if x >= 30 + side_w + 100 then
            Curr_color = 'black'
            Curr_time = 0
          end end end end

I'm going by the description in https://www.britgo.org/bgj/10643.html, but I haven't actually seen a Go clock before, so feedback appreciated.