Search terms tried so far in various combinations: history driver's licenses, driver's license photos, photo ID history/technology, old driver's license, driver's license history US, Texas driver's license, Arizona et al. I'm getting a lot of pages on how to request your own license history or take a license photo that won't frighten small children. 'Photo ID' mostly nets information on passports (photos weren't required until 1915, FYI), fake ID and current political controversies.
But I have turned up some images of various state licenses from the 1950s and early 1960s that have no photos, only a physical description. I also found a document from the Oregon DMV that mentions photo licenses being issued beginning in 1975. That seems to imply that the technology for photo licenses was developed around the middle 1970s, and that probably most states began to require photos in that general time period. But Texas is frequently a law unto itself, especially where driving is concerned, so it may not be safe to extrapolate. :)