Slide projectors with the timed automatic mode are almost as old as remote control projectors themselves. The Revere 808 (Not necessarily the first timed automatic projector) was introduced in the mid-1950s. Kodak's Cavalcade series would include the feature soon after.
The feature did not really meet its potential until the Kodak Carousel 550 hit the market in the early sixties. Automatic operating was of little benefit when all slide trays were straight, because an automated show would end when the last slide was shown. With the Carousel, the tray could continue the show indefinitely. The competing Sawyer's Rototray design followed suit.
These US Carousel models had timed automatic operation:
550 (the first Carousel), 570, 800, 800H, Custom 800H, 850, 850H, Custom 850H, 860, 860H, Custom 860H, 5400 and 5600, as did many Rototray models (I believe all Sawyer's 7xx models, the higher-end GAF-branded and Nikkormat-branded models).
Sorry I don't know which projectors in the European market have both timed operation and circular trays. The North American and European markets for slide projectors somehow became quite isolated from each other.
One caution about automated slide projection: projection of a slide does affect the dye image, and too much projection can cause fading, which may be color selective (changing the color balance of the slide). Counterintuitively, Kodachrome slides, with their legendary color permanence in dark storage, fade faster than E-6 slides in the projector gate, turning cyannish as the magenta dye is diminished.