According to my tests and these three pages, multi-layer or multi-page TIFFs have the PageNumber tag and transparent TIFFs have the ExtraSamples tag set to either 1 or 2.
Once you know this it is easy to use ExifTool to move both multi-page and transparent TIFFs into a separate directory:
exiftool -if "(($PageNumber) || ($ExtraSamples#>0))" -directory=Moved *.tif*