An on-board oscillator and a 17-stage divider compose IC1. By connecting a standard 3.58-MHz, television color-burst crystal as shown, an accurate source of 60-Hz squarewaves is generated at the IC`s output, pin 1. Those pulses are then fed to IC2, a 4024 seven-stage ripple counter. Its outputs are connected to different gates in IC3, which is a dual four-input NAND gate.
Crystal-timebase - schematic

Depending on which position pulse-select switch S2 is on, one of those gates will provide an output/reset pulse of the selected width.

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