wedidntstartthefire

So I'm trying to add the Previous/Next links to my Navlinks Module using a code that was previously posted here, but I'm having issues with the Previous link showing up regardless of whether or not there's previous entries (I'm testing on this journal with public entries for reference).

The code I'm using in my theme layer is this:

# code by ninetydegrees/foxfirefey
function print_module_navlinks() {
 
  var Page p = get_page();
  var string prev_link;
  var string next_link;
  
  if ( $p isa EntryPage ) {
      var EntryPage ep = get_page() as EntryPage;
      var Entry e = $ep.entry;
      var Link prev = $e->get_link("nav_prev");
      $prev_link = """<a href="$prev.url">$prev.caption</a>""";
      var Link next = $e->get_link("nav_next");
      $next_link = """<a href="$next.url">$next.caption</a>""";
  } elseif ( $p isa DayPage ) {
      var DayPage dp = get_page() as DayPage;
      $prev_link = """<a href="$dp.prev_url">$*text_day_prev</a>""";
      $next_link = """<a href="$dp.next_url">$*text_day_next</a>""";
  } elseif ( $p isa RecentPage ) {
      var RecentPage rp = get_page() as RecentPage;
      if ( $rp.nav.backward_count > 0 ) { 
          $prev_link = """<a href="$rp.nav.backward_url">""" + get_plural_phrase( $rp.nav.backward_count, "text_skiplinks_back" ) + "</a>"; 
      }
      if ( $rp.nav.forward_count > 0 ) { 
          $next_link = """<a href="$rp.nav.forward_url">""" + get_plural_phrase( $rp.nav.forward_count, "text_skiplinks_forward" ) + "</a>"; 
      }
  } elseif ( $p isa MonthPage ) {
      var MonthPage mp = get_page() as MonthPage;
  	if ($mp.prev_url != "") { $prev_link = "<a href='$mp.prev_url'>Previous</a>"; }
  	if ($mp.next_url != "") { $next_link = "<a href='$mp.next_url'>Next</a>"; }
  }

var string[] navlinks_order = [];
  var string{} navlinks_urls = {};
  var string{} navlinks_text = {};
 
  $navlinks_order =
    [
        "entries",
        "archive",
        "read",
        "profile",
    ];
 
 $navlinks_urls =
    {   "profile" => "$p.base_url/profile",
        "entries" => "$p.base_url",  
        "archive" => "$p.base_url/archive",
        "read" => "$p.base_url/read",

};
 
 $navlinks_text =
    {   "profile" => "Profile",
        "archive" => "Archive",        
        "read" => "Read",        
        "entries" => "Recent",      
        
    };

open_module("navlinks", "", "");
    var string[] links = [];
    
    if ( $prev_link ) {
        $links[size $links] = $prev_link;
    }    
    
    foreach var string k ($navlinks_order) {
        if ($navlinks_urls{$k} != "") {
            var string css = """ class="$k" """;
            if ($p.view == $k) { $css = """ class="current $k" """; }
            $links[size $links] = """<a href="$navlinks_urls{$k}"$css>$navlinks_text{$k}</a>""";
        }
    }
    
    if ( $next_link ) {
        $links[size $links] = $next_link;
    }
     
    
    print_module_list($links);
    close_module();
}