I assume
GoogleMapForASPNet is a custom control you have and has a javascript method which initializes the map (like loadMap(), initMap() or DrawGoogleMap() as in Shabdar's
article or ...) then add
OnClientClick attribute to the tab containing googlemap:
<asp:panel id="Panel3" runat="server" OnClientClick="DrawGoogleMap">
which
DrawGoogleMap() should be the actual function that initializes your map and remember not to include parentheses here.
This makes the map being shown when user clicks on the tab.
And don't be surprised when it works despite the fact the caller and callee are in different controls. It happens because in actual rendered page you can access all javascript functions by their original name.
And one last hint is that you can use a hiddenfield to save a value indicating whether the map has already been initialized or not so every time the user reopens the tab, the map doesn't blink and reset to it's initial location.