I've downloaded and set up a basic SMF installation. Finding the file(s) that would need modifying was a doddle.
Themes\default\language\index.english.php has the string:
$txt['totalTimeLogged1'] = 'Total time logged in: ';
It is used in Themes\core\index.template.php (search for totalTimeLogged1):
// If the user is logged in, display stuff like their name, new messages, etc.
if ($context['user']['is_logged'])
{
echo '
<ul class="reset">
<li><a href="', $scripturl, '?action=unread">', $txt['unread_since_visit'], '</a></li>
<li><a href="', $scripturl, '?action=unreadreplies">', $txt['show_unread_replies'], '</a></li>';
// Is the forum in maintenance mode?
if ($context['in_maintenance'] && $context['user']['is_admin'])
echo '
<li class="notice">', $txt['maintain_mode_on'], '</li>';
// Are there any members waiting for approval?
if (!empty($context['unapproved_members']))
echo '
<li>', $context['unapproved_members'] == 1 ? $txt['approve_thereis'] : $txt['approve_thereare'], ' <a href="', $scripturl, '?action=admin;area=viewmembers;sa=browse;type=approve">', $context['unapproved_members'] == 1 ? $txt['approve_member'] : $context['unapproved_members'] . ' ' . $txt['approve_members'], '</a> ', $txt['approve_members_waiting'], '</li>';
// Show the total time logged in?
if (!empty($context['user']['total_time_logged_in']))
{
echo '
<li>', $txt['totalTimeLogged1'];
// If days is just zero, don't bother to show it.
if ($context['user']['total_time_logged_in']['days'] > 0)
echo $context['user']['total_time_logged_in']['days'] . $txt['totalTimeLogged2'];
// Same with hours - only show it if it's above zero.
if ($context['user']['total_time_logged_in']['hours'] > 0)
echo $context['user']['total_time_logged_in']['hours'] . $txt['totalTimeLogged3'];
// But, let's always show minutes - Time wasted here: 0 minutes.
echo $context['user']['total_time_logged_in']['minutes'], $txt['totalTimeLogged4'], '
</li>';
}
if (!empty($context['open_mod_reports']) && $context['show_open_reports'])
echo '
<li><a href="', $scripturl, '?action=moderate;area=reports">', sprintf($txt['mod_reports_waiting'], $context['open_mod_reports']), '</a></li>';
echo '
</ul>';
}
Contrary to what I suggested I'm thinking it might be easier to insert a line in the second file immediately after
<li><a href="', $scripturl, '?action=unreadreplies">', $txt['show_unread_replies'], '</a></li>';
I'll have a go in the next day or so and if it works let you have the URL to have a look and give you the code. If it just comes down to inserting a single line it would be easy to take it out before you attempt any upgrade/patch and then re-add it after which would reduce the risks.
Edit: It wouldn't need the "(logged in users only)" as the bit I'm suggesting adding to is only displayed for logged in users.