Re: Well the requirements of loading data overlap with the requirements for audio
If you plonked 5V into the "MIC" socket of a standard cassette recorder of that time you'd get a click on the tape, probably oversaturate the tape briefly too, though that depends on the auto level control. Following it by 0V doesn't guarantee "no dc component" it guarantees an average level of 2.5V. That said, there was probably a capacitor somewhere in the input circuitry (if not in the output of your board) so no dc would actually get through to the recording circuit.
What you would record would probably be a crude sine wave - a square wave shaped by the response of the capacitor(s) inline and how the FM circuitry dealt with such abuse - and playing it back through a speaker would result in a nasty two-tone buzz; a "high frequency" and "low frequency".
If your "ticks" were (let's say) at 2kHz, a string of "1"s would result in a 1kHz buzz while a string of "0"s would buzz at 500Hz.
The circuitry for reading it wouldn't be reading "5V" or "0V" directly - the output circuitry of the cassette recorder wouldn't allow that, and anyway it would be affected by the level of the volume control - the input circuitry on your Z80 board would possibly have been some kind of Schmidt-triggered "AND" gate or S/R flip flop, though I'd need to think about how to deal with "1"s arriving at twice the rate of "0"s. Was it actually "HLHL" for "1" and "HHLL" for "0"?
If you read down the article I linked about the Kansas City Standard it notes that while the original standard used was four cycles of 1,200Hz for "0" and eight cycles of 2,400Hz for "1", faster developments such as the version used on the BBC Micro used one cycle of 1,200Hz for "0" and two cycles of 2,400Hz for "1" which is conceptually similar to your scheme.
Yes, I remember the flashing square too. I don't think it was Spectrum code, but another kind of "agnostic" format that could be loaded into any one of several supported machines. I seem to remember that the sensor was a simple phototransistor connected to a data line, 5V and 0V. Simple and safe enough on a machine such as the BBC Micro which had a "proper" user port (or was the joystick port or maybe even the lightpen input used?) but dangerous on a Spectrum where the edge connector was the unbuffered lines direct from the micro inside. Of course, for a relative youngster such as I, sending off to Maplin for a single phototransistor, resistor, wire and maybe one of those connectors was a bit silly when you added the P&P, and I didn't get into Cardiff often enough to visit Mr. Marks in Wyndham Arcade in time to build something.
Dare say it would have survived video recording too, but we didn't have a VHS player until much, much later.