Don't forget to load all bindings when constructing an external context - this constructor was added for precisely this reason, after all.

Source/OpenTK/Graphics/GraphicsContext.cs

@@ -157,6 +157,8 @@ namespace OpenTK.Graphics
                 }
 
                 available_contexts.Add((implementation as IGraphicsContextInternal).Context, new WeakReference(this));
+
+                (this as IGraphicsContextInternal).LoadAll();
             }
         }