By default you will not have permissions to an External Content Type within SharePoint 2010, even if you have built and deployed it. You need to go to the Business Connectivity Services administration page and give the necessary users the permissions they need.
1, Open Central Administration
2, Click the Manage Service Applications link
3, From the list of services, click the Business Data Connectivity Service.
4, Using the context menu that appears when you hover your mouse over your External Content Type you can set the permissions:
Upon setting the permissions you should then be able to access your external data in an External List or BCS Web Part. Be aware that the permissions are sometimes cached so may take a minute or two to update.