To change a line in Google Earth when you mouse over or hover on it then you need the KML to define a StyleMap that with a style for "normal" mode and another for "highlight" mode.
In the example below, the line shows a thin blue line by default showing the normal style, but changes to a thicker purple line when you hover the mouse over the line which then switches to the highlight style.
Example:
<?xml version="1.0" encoding="utf-8"?>
<kml xmlns="http://www.opengis.net/kml/2.2">
<Document>
<Style id="sn">
<LineStyle>
<color>7fff0000</color>
<width>2</width>
</LineStyle>
<PolyStyle>
<color>7fff0000</color>
</PolyStyle>
</Style>
<Style id="sh">
<LineStyle>
<color>7fff00ff</color>
<width>8</width>
</LineStyle>
<PolyStyle>
<color>7f00ff00</color>
</PolyStyle>
</Style>
<StyleMap id="msn">
<Pair>
<key>normal</key>
<styleUrl>#sn</styleUrl>
</Pair>
<Pair>
<key>highlight</key>
<styleUrl>#sh</styleUrl>
</Pair>
</StyleMap>
<Placemark>
<name>Style Map example</name>
<styleUrl>#msn</styleUrl>
<LineString>
<tessellate>1</tessellate>
<altitudeMode>absolute</altitudeMode>
<coordinates>
-112.265654928602,36.09447672602546,2357
-112.2660384528238,36.09342608838671,2357
-112.2668139013453,36.09251058776881,2357
-112.2677826834445,36.09189827357996,2357
-112.2688557510952,36.0913137941187,2357
-112.2694810717219,36.0903677207521,2357
-112.2695268555611,36.08932171487285,2357
-112.2690144567276,36.08850916060472,2357
-112.2681528815339,36.08753813597956,2357
-112.2670588176031,36.08682685262568,2357
-112.2657374587321,36.08646312301303,2357
</coordinates>
</LineString>
</Placemark>
</Document>
</kml>