Is there a relatively easy to use tool that will allow me to demosaic some raw data stored in a TIFF file (not a standard raw file such as DNG, NEF, etc.), assuming a Bayer pattern? The TIFF contains no metadata, so should be possible to specify any necessary additional information separately.
Most raw formats are actually stored in .tiff containers. They're simply proprietary data in a .tiff container.
Three thoughts for you for what you are trying to do:
1) Try Dave Coffin's DCRaw package, without or with a GUI front-end.
2) You could also read the file into Photoshop as a (.raw) format; it would come in as a single plane and require manipulation to be converted to RGB.
3) If you are or know a programmer, it would not be hard to parse this from a simple TIFF file without any metadata (perhaps an hour's work or so).