The single-pusher chronograph is the oldest form of mechanical chronograph: a single button governs the three phases of measurement — start, stop, and reset — through successive presses. Single-pushers came first, then two-pushers appeared in the Thirties. This isn't a simplification: it's a precise constructive choice, with mechanical consequences that are anything but trivial.
The mechanism relies on an internal sequencer that memorizes the chronograph's state with each press. In quality movements — and I'm thinking of historic Minerva, Angelus caliber A5000, De Bethune — that sequencing is entrusted to a column wheel. The column wheel is the component that reliably establishes the start-stop-reset order: the teeth of the column raise or lower the clutch and reset control levers with a precision that a cam system cannot replicate. Without a column wheel, the single-pusher works, but with less precision during state changes.
The difference from the two-pusher is conceptual as much as aesthetic. With two buttons — one for start/stop, one for reset — the functions are separated and you can't accidentally reset an ongoing measurement. With the single-pusher, one extra press wipes everything. It demands attention. This is why some consider it a tool for those who truly know their watch.
The button can be positioned in very different ways: integrated into the crown (Minerva, Hermès H08, Ming 57.04), positioned at 2 o'clock in classic tradition, or — in so-called left-handed watches with crown at 9 o'clock — at 9:30 or on the case's left side. In certain cases, like the Bremont mentioned in the sources, the single-pusher governs not the chronograph but the perpetual calendar: same sequencing principle, different function.
I've restored dozens of single-pusher movements from the Thirties and Forties. The recurring problem is never the pusher itself: it's the return spring, which fatigues and produces anomalous pressure on the sequencer. In modern single-pushers derived from original two-pusher calibers — like the reworked Valjoux 7750 from Albishorn — you must verify that the sequencer modification is robust: not all manufacturers handle that conversion well.