An overview of this issue.
I did not understand your previous response.
1) question below.
yes #categories a.catBoxHeading1, is working, Thank You
with some inheretence from .sideBoxContent
and .category-top-text, not working.
.sideBoxContent still overrides .category-top-text.
=
mywebsite html from View Page Sorurce see <span class="category-not-selected">
<h3 class="leftBoxHeading" id="categoriesHeading">Products</h3>
<div id="categoriesContent" class="sideBoxContent">
<a class="catBoxHeading1" href="http://www.mywebsite.com/index.php?main_page=index&amp;cPath=28&amp;zenid=123456789">&gt;Air Conditioning<br />Split System<br />Ducted<br /><br /></a>
<a class="category-top-text" href="http://www.mywebsite.com/index.php?main_page=index&amp;cPath=29&amp;zenid=123456789"><span class="category-not-selected">Split Systems <br />AC Ducted<br />1 to 2 Tons<br /><br /></span></a>
<a /* Column left continues with both Headings and cat links*/
==
In CSS style sheet
.catBoxHeading1---- line 913
.category-top-text--line 937
.sideBoxContent-----line 944
===
One question here.
My tpl_categories.php as it is now.

$disp_block = '';
//$disp_block = '<br />'; //if not using display: block; in stylesheet, uncomment this line
$content = "";

$content .= '<div id="' . str_replace('_', '-', $box_id . 'Content') . '" class="sideBoxContent">' . "\n";
for ($i=0;$i<sizeof($box_categories_array);$i++) {
switch(true) {
//1 Question)Do I need to add .catBoxHeading1 and .category-top-text here as a $new_style=
// or #categories a.catBoxHeading1 as a $new_style= .

case ($box_categories_array[$i]['top'] == 'true'):
$new_style = 'category-top';
break;
case ($box_categories_array[$i]['has_sub_cat']):
$new_style = 'category-subs';
break;
default:
$new_style = 'category-products';
}

<!--bof-optional categories tabs navigation display-->
<div id="navCatTabsWrapper">
<div id="navCatTabs">
<ul>
<li><a class="category-top" href="http://www.mywebsite.com/index.php?main_page=index&amp;cPath=28&amp;zenid=123456789">Split System <br /> AC Ducted<br />1 to 2 Tons<br /><br /></a> </li>
This <ul> contains all the non heading cat links
<li><a class="category-top" href="http://www.mywebsite.com/index.php?main_page=index&amp;cPath=106&amp;zenid=123456789">Packaged AC<br />Heat Pumps</a> </li>
</ul>
</div>
</div>
<!--eof-optional categories tabs navigation display-->

overview ends

Thank You
Relentless