Tape sync, also known as FSK sync (as it involves binary frequency-shift keying) is essentially DIN sync, once it's been modified to be tape friendly. Whereas DIN sync uses two different signals, the clock pulse signal and the run/stop signal, tape sync has to combine these into one signal, to fit on a single channel of a multitrack tape recorder. The stunningly simple way it does this is by completely ignoring the clock pulses when run/stop is low, and faithfully recording them when run/stop is high, starting with the next pulse.
If you're wondering why it doesn't cause problems that the sequencer doesn't know which tempo it's playing at until after it's started playing, bear in mind that it doesn't ever know which tempo it's playing at. Only the clock is concerned with the timing of the pulses. The sequencer merely counts them.
The next part of making the signal tape friendly, now that it fits on a single channel, is to guarantee it's in an audible frequency that audiotape can be reasonably expected to record and play back, regardless of the tempo. This simply involves modulating it with a square wave, which is a lot easier to do than it sounds. When the clock pulse is high, a high frequency square wave is played; when the clock pulse is low, a comparatively low frequency square wave is played.
The exact frequencies seem a bit hazily defined. Roland, who made several machines that use tape sync, claim they're "approximately" 2100Hz and 1300Hz (see MC-4 Service Notes, page 4), while most sources on the web claim they're 2400Hz and 1200Hz respectively (see An Introduction to Tape/MIDI Sync and the MQX-32 and Sync or Swim?).
So tape sync consists of a short, roughly 1kHz tone telling you to get ready, then a steady switching back and forth between 2kHz and 1kHz tones. Every time you count twenty-four such switches to the higher tone and back again, a quarter note has passed.