Working from NaN0's mod, this will add a column titled "Last Updated" directly before the Client/Staff column, which reflects the date of the last message or response. Additionally, if the Client is the last responder, the time and word "Client" will be boldfaced and red.
In include/staff/tickets.inc.php, CHANGE this:
<a href="tickets.php?sort=date&order=<?=$negorder?><?=$qstr?>" title="Sort By Date <?=$negorder?>">Date</a></th>
<th width="250">Subject</th>
to this:
<a href="tickets.php?sort=date&order=<?=$negorder?><?=$qstr?>" title="Sort By Date <?=$negorder?>">Date</a></th>
<th nowrap>Last Updated</th>
<th>By</th>
<th width="250">Subject</th>
then further down, CHANGE this:
<td align="center" nowrap><?=Format:($row)?></td>
<td><a <?if($flag) { ?> class="Icon <?=$flag?>Ticket" title="<?=ucfirst($flag)?> Ticket" <?}?>
to this:
<td align="center" nowrap><?=Format:($row)?></td>
<? $ticket = new Ticket($row);
if ($ticket->getLastReplyRespondent()) {?>
<td nowrap style="color;font-weight">
<?=Format:($ticket->getLastMessageDate())?></td>
<td style="color;font-weight">Client
<?} else {?>
<td nowrap><?=Format:($ticket->getLastResponseDate())?></td>
<td>Staff
<?}
?> </td>
<td><a <?if($flag) { ?> class="Icon <?=$flag?>Ticket" title="<?=ucfirst($flag)?> Ticket" <?}?>
Sorting for the "Last Updated" column seems to be next in order, if anyone else want's to tackle that.