EUREAKA! FOUND THE MAKE OF THIS MACHINE (Another Online Sewing Machine Group).
Posting the UNICORN image produced an exact match. It’s a version of a NEW PROCESS (Mfg FREE) of Rockford, Illinois. She also referred to it as New Rockford L-Head.
She showed images of an exact match to my grandmother’s machine right down to the UNICORN on the machine base! They found it in someone’s yard, rusting as Yard Art. They are currently restoring it and using it eventually.