I'm guessing that Stevecast isn't fully aware of how bases are defined in Orbiter. MassDriver is built for Orbiter 2005, and bases are handled differently starting with Orbiter 2006.
Prior to 2006, for a base to be recognized by the core, it needed to be listed (along with it's location) in the surfbase section of the planet (or moon's) config. Editing your Moon.cfg was required to add a new base. None of these add-ons actually add a new base, they replace an existing one. No new entry on the surfbase list would be required. It's important to note that the bases location is defined in Moon.cfg, not Brighton.cfg.
Further, starting with Orbiter 2006 bases no longer need be defined in the planet or moon's config. The bases location is now defined in the base config. Installing MassDriver overwrites the stock Brighton.cfg with one designed for Orbiter 2005. It does not contain the base location. It won't "show up" because Orbiter doesn't know where to put it. Specifying the location in the surfbase section of the moon.cfg may solve this - if you wanted to install the MassDriver in it's original form.
The only file you should need to edit is Base.cfg to add the textures as instructed by the Brighton Base Enhancement. Also, the last thing you will do is place the Brighton.cfg supplied by Stevecast into the Orbiter/Config/Moon/Base folder, overwriting the one that's there already. Unless you've altered your Moon.cfg and changed the base directory paths, this should take care of everything except the MassDriver itself, which is a vessel and must be included in the scenario file.