Oh, well the main quoteit page uses quote_listquote so that won't be affected. To differentiate between random quotes you'll need a conditional in quote_randomquote, something like this:
HTML Code:
<if condition="THIS_SCRIPT == 'forumdisplay'">
(everything in the standard quote_randomquote template)
<else />
$quotelistbit
</if>
I'm not sure if forumdisplay is the right value to use though, you'll need to check forumdisplay.php (it should be right at the top).