A possible workaround would be subscribing to the selectedIndexChanged event of the search context dropdown. This can be done in the OnClientLoad event of the SearchBox: 

function OnClientLoad(sender, args) {
    var context = sender.get_searchContext();
    var $ = $telerik.$;
    $(context).on({
        "selectedIndexChanged": function (event) {
            var searchbox = $find("<%= RadSearchBox1.ClientID%>");
            // this is the search context dropdown selectedIndexChanged event handler 
        }
    });
}