I have a very unpopular theory that, because "Tadeo Gomez" had various different handwriting styles, use different fonts and potential looked to have "signed" necks both left-handed and right-handed, that he infact did sign them all personally but they were signed in his name by various people with him - as shift foreman and leading hand.
I know this is unpopular because TG, Tad or Tadeo Gomez has been elevated to legendary super luthier status, and even the smoothed neck volute has been named after him: the Tadeo Taper, and people don't life the mythical bubble bursting.
But ask yourself this: Do you sign your name in different fonts and styles and use both left and right-hand the make that signature? No? Then why should Mr. Gomez?
I do believe he was a very skilled worker but he wasn't what we call a master luthier we know today.
So my answer. Mr. Gomez may have signed your neck (and body); or it may have been someone else on his behalf.

Peter
Disclaimer. This is my theory. Not proven; nor has any other theories about Mr. Gomez or others in those early Fullerton days.