Tested, and won't work under on OnLapperStart Event.
Try
Event OnConnect( $userName ) # Player event
$ShortTime = getLapperVar( "ShortTime" );
$LongTime = getLapperVar( "LongTime" );
$ShortDate = getLapperVar( "ShortDate" );
$LongDate = getLapperVar( "LongDate" );
openPrivButton( "shorttime_button",90,80,20,4,4,-1,32,$ShortTime);
openPrivButton( "longtime_button",90,85,20,4,4,-1,32,$LongTime);
openPrivButton( "shortdate_button",90,90,20,4,4,-1,32,$ShortDate);
openPrivButton( "longdate_button",90,95,20,4,4,-1,32,$LongDate);
EndEvent
It's also possible to combine 2 of these variables to give you time and date.
Try add these;
openPrivButton( "shorttimeanddate_button",85,100,30,4,4,-1,32,$ShortTime . " on " . $ShortDate);
openPrivButton( "longtimeanddate_button",83,105,36,4,4,-1,32,$LongTime . " on " . $LongDate);