They have had push button transmission before. I forgot who had them in the 50s and 60s but they had similar problems.
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In ‘58, a couple of girls I knew came to pick me up in a Mercury convertible. The push button shifting was located in the center of the steering wheel. I was given the chance to drive it and it was really awkward, since I’d only driven stick shifts before.
By the way... The photo in #4 above shows a “D/S”. What does the “S” mean?
Sport
Car shifts gears at higher RPM
Most of the time - and I don't know that breed of car to be absolutely sure - that would be “D” (automatic transmission” and “S” or “Standard - where the lever drops into a manually-controlled mode kinda of like a standard transmission. If you are in “D” you drive like a “normal” automatic transmission.
Go to “S” standard (or “M” manual mode on other cars), then the transmission thinks it is an automatic after 1st gear. Usually, you drop into that mode, then bump the shift lever sideways to go up or down 1 gear. Lets you pretend you are actually shifting gears.