Hi Daniel,
It has been a while since I tried this, so the details are a bit vague.
I think you need to explicitly tell EA to display the behavior, either directly or by enabling a partition on the element.
When EA does this via the UI, I think it stores the setting in one of the PDATA fields of the DiagramObject. For elements, it is possible to read these via the MiscData attributes, but not to set them. There is no such thing for DiagramObjects. To make matters worse, the Style attribute is write-only (i.e. you cannot use it to inspect the current state) and does not let you address the settings you need.
So, where does that leave you?
I think you need to open the database itself. If you are not using the Desktop Edition of EA (and perhaps if you are) you can do this by creating a connection to outside of EA (even in the same program). Remember to open the second connection with shared access if you want EA to be able to use the model at the same time (or if you also have it open through EA in your code). You can use the Repository.ConnectionString property to get a workable string, but remember to remove the EA prefix.
Now find the correct DiagramObject record in the t_diagramobjects table. Read the ObjectStyle field.
[Some notes: In an EAP file this is a Text field with a maximum length of 255. Other repositories might be more forgiving, but if you will (ever) transfer to an EAP file you must respect this limit. Jet sets Unicode Compression to Yes for text fields; this should not usually affect your application but it might be worth noting. This field can be null, so you should be prepared to gracefully handle this possibility.]
The field contents are a list of settings - these are not documented, so don't ask me - that control a variety of display options. The settings are semicolon delimited. Most (but not all) settings are only present when they are not set to the default value (or the 'off' setting). They might show up if they have been set, and later restored to default values. You will need to add the settings you need, then save the record. After that you will need to refresh or reload the diagram, package, or model in EA if you want to see your changes in real time. See the API documentation for how to handle that.
To learn the correct syntax you need to do some experimentation. Create a diagram by hand. On the diagram set up an element with behavior showing, as you would want your application to render it. Now close the model and open it with MS Access (or any other tool that allows you to read the schema). Check out the field contents. It will be pretty obvious which settings you need.
HTH, David