Enabling ScriptManager PageMethods doesn’t work in some scenarios in SharePoint 2013

I worked on a case where the problem was that PageMethods won’t execute from within a SharePoint 2013 application page (page deployed to the _layouts folder).  To replicate the problem, I had a custom master page deployed through a VS 2012 solution with the following definition within the <body/> element. <asp:ScriptManager id="ScriptManager" runat="server" EnablePageMethods="true" EnablePartialRendering="true"…

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