Unfortunately the UI only shows String and primitive-type properties in user-created rules/plugins. Yet some built-in rules/plugins use enums... how can this be? Thanks to the magic of the disassember and some detective work, we discover that it only accepts enums whose assembly name contains the string "Microsoft.VisualStudio.QualityTools.WebTestFramework".
So if you go to the trouble of compiling your enums (or indeed, your entire project) into an assembly called, for example, "MyEnums.Microsoft.VisualStudio.QualityTools.WebTestFramework", BOOM your enum-typed properties will happily appear in the editor UI.