Good suggestion, @philip1009. I did some investigating by opening up the iLogic browser and running the following code, to see if it would reveal the name of the iLogic browser:
For Each oBrowserPane In ThisDoc.Document.BrowserPanes
MessageBox.Show(oBrowserPane.Name)
Next
...It worked, but the only names it showed were "Favorites" and "Model", so apparently the iLogic browser isn't part of a document's "BrowserPanes" collection, even if it's open.
(Oh and yes, just telling people to open it would be simple enough, but we're automating several other things with this rule and we'd like to automate opening the iLogic browser as well, if possible).
Any more suggestions?