Without over complicating it, I wonder if you had a flexible second hand like a spring, that's just a bit too long, with pins on the 5 second hand, dots on the

Without over complicating it, I wonder if you had a flexible second hand like a spring, that's just a bit too long, with pins on the 5 second hand, dots on the rest and decent motor to drive the shaft. As the shaft turns the spring builds up tension and eventually bends enough to jump past the pin.