I did go through the 'perlmod' to find the part about BEGIN executing as soon as parsed

If you didn't realize that, then I'm curious as to why you placed parsing Glb first in both scenarios? It seems to indicate you knew use Glb; was executed as soon as it was parsed.

If you knew that, the key point you were really missing was that require and thus use execute the module as any other script. It gets parsed and executed. That's got nothing to do with BEGIN.