Добавьте ImageButtion как ExpandControl и используйте событие keyup textbox для расширения расширителя на стороне клиента:
function expand() {
var extender = $find("CollapsibleExtender1");
if (extender.get_Collapsed()) {
$find("CollapsibleExtender1").expandPanel();
}
}
<asp:Panel runat="server" ID="CollapsiblePanel">
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</asp:Panel>
<asp:ImageButton runat="server" ID="MyImageButton" ImageUrl="~/Images/infoindicator.gif" />
<asp:Button runat="server" ID="MyButton" Text="Click Me" OnClientClick="expand(); return false;" />
<ajax:CollapsiblePanelExtender ID="CollapsiblePanelExtender1" runat="server" BehaviorID="CollapsibleExtender1"
ExpandControlID="MyImageButton" Collapsed="true" TargetControlID="CollapsiblePanel"
CollapsedText="Collapsed" ExpandedText="Expanded" SuppressPostBack="true" />