Friedrich has featured the auto-fan option (Money Saver® button)for many years, although not on all models, and electronic controls aren't a necessity to allow the feature. HUGE-capacity, 36,000 BTU, through-the-wall cool/heat units were in several stand-alone classroom buildings at my school dating to the 1970s had auto-fan. A few teachers used it, most didn't.
Grandmother has a 16K btu heat/cool unit with analog controls and auto-fan option (selected by me at the time of purchase). Interestingly, the auto-fan setting on Friedrich units typically maintains a more consistent temperature than continuous fan. They have an anticipator heater on the thermostat bulb to moderate the temperature swing, which I believe is activated for auto-fan and deactivated for continuous fan.