"I was taught that a genuine Rolex doesn't tick and must have a smoothly sweeping second hand."

Well, yes actually they do tick. It's a common misconception that a Rolex with a ticking second hand is a sign of a fake. This can be very misleading when looking at vintage Rolex.

If you inspect a Rolex watch closely under magnification with a jewelers loupe, the second's hand DOES tick many times per second. Even modern Rolex do this, albeit imperceptibly. Unlike some other high-end luxury watches, it is not a perfectly smooth sweeping motion. This is especially noticeable in vintage Rolex watches with their older movements.

The number of ticks per second is a function of the movements “beat rate”, usually measured in Hertz (Hz) or vibrations per hour (VpH). Hertz refers to the number of oscillations that the balance wheel in a watch’s movement makes in a single second.

A frequency of four Hz makes four full oscillations per second, or eight vibrations, which adds up to 28,800 vibrations per hour.

Vintage Rolex movements typically beat at 18VpH. More contemporary Modern Classic Rolex movements beat at 21 and 28 VpH. By comparison, quartz movements are orders of magnitude more precise with quartz crystal vibrating at 32,768 Hz.

In 2019, Zenith introduced the Defy Inventor, a limited-edition mechanical watch with a movement that hits 18 Hz (129,600 vph!)

Legitimate Rolex models DO tick. Some are more obvious than others. For example, all the Oysterquarts models tick thanks to their quartz movements.

Yes, Rolex made battery-powered quartz watches!

The reference few people know about is the Rolex Tru-Beat Reference 6556, with a rare “deadbeat seconds hand”. This is a mechanical movement designed to tick once per second.

The 6556 was designed specifically for physicians to aid the measurement of a patient's pulse rate (heart beat). Like the later Rolex Oysterquartz, it ticks once per second thanks to a remarkably complex mechanism, based on caliber 1040.

Deadbeat seconds also called dead seconds or jumping seconds is a mechanical marvel known only to hardcore vintage enthusiasts. Introduced in 1954, it was a commercial flop despite being a remarkable engineering achievement.

Being rare and relatively unknown are characteristic hallmarks of great collectible models, and in 2015 the famed Philips auction house sold one for US$40K

CONCLUSION

YES, genuine vintage Rolex genuinely tick, while most modern models tick imperceptibly.