I contacted ESRI support and they confirmed that when a Windows Form is modeless that the Tab key does not work for a Combobox that has AutoComplete settings other than None and a populated list. I have asked them to file a bug report for that behavior.However, the Tab key does work with both the AutoComplete Combobox and my custom component in a Windows Form when the Form is Modal. For my particular project I can use the Modal Dialog (launching the Form with ShowDialog instead of Show).My custom component still has Tab problems with a DockableWindow, so I cannot use a DockableWindow unless I can come up with a way to make that work. But since that component is not a standard windows control I do not expect ESRI can offer me much help, so for now I am not going to use a DockableWindow.So the Modal Windows Form is the only available solution at this time, in case this comes up for anyone else.