Back in the day bassists played exclusively with their thumb, so the rest, actually called a grip bar back then, was below the G so you could anchor with your fingers. As times progressed and finger play came into being, the grip bar moved up over the E as a thumb rest. Some, like my 67 Coronado II, have both.
Looking through the thumbnails of my collection, I see grip bars all the way through my 73 Tele. I have nothing between that and my 78 Musicmaster which has a thumb rest. My next bass is a 78 Bullet and it has neither, nor does any bass I own from there through today.
Hope this helps.
Fender collection includes Precision,Jazz, Coronado II,Mustang,Tele,Musicmaster,Bullet,Katana,Performe r,DR4,Factor,JP90,Prodigy,Prophecy I,Urge,Urge II, Kingman. Have a couple non Fenders too.