[1] https://polgote.com/en/blog/time-controls-go-byo-yomi-fische...
Yes, I'm aware that traditionally instead of main time you'd have a large (for important slow games) number of one-minute periods. Using multiple byoyomi periods is even stranger - more complex for questionable effect on time management strategy.
One idea I've had that I'd like to see implemented is "reverse single byoyomi": you have a certain amount of time per move (which resets for each move), and when exceeded on a given move you start using your "main time" (and lose when that runs out). I think that fixes the above problems: you can spend a little time on each move (but you and your opponent can expect reasonably brisk play from each other most of the time), and if you prefer you can use your reserve in late game to count the score, double-check for teire and semedori, etc. And, of course, you don't encounter extra time pressure just because the game went to an unusually high number of moves (and your opponent doesn't get to waste huge amounts of time during dame-filling just because the game went to an unusually low number of moves).
Fischer is close to accomplishing this, but it makes you "bank" and manage your thinking time for the longer moves.
Like the article says, with Fischer you always have the opportunity to claw back extra time, so it's not as severe a deficit.
What's so special about move 40? If you analyze chess games, you'll probably find that moves 40-45 are on average more accurate than moves 35-39 even it feels this number shouldn't be part of the game.
In the chess world there are two delay systems used as an alternative to Fischer timing: Bronstein timing and simple delay timing. I don't know how common Bronstein delay is. In the US simple delay is the recommended timing method for USCF events.
Fischer and Bronstein (which is several years older than Fischer) are very similar. The difference is that if the increment (Fischer) or delay (Bronstein) is N seconds and the move took T seconds, Fischer unconditionally adds N seconds whereas Bronstein adds min(N,T) seconds.
For example if you were playing with a 5 second increment or delay and your move takes 12 seconds than you clock ends up at 7 seconds less than where it started.
If your move took 3 seconds your clock would end up 2 seconds above where it started in Fischer and back to where it started in Bronstein.
Simple delay simply delays the start of the clock by the delay amount. For example if playing with a 5 second simply delay when it becomes your turn your clock simply waits 5 seconds before it starts counting down. If you move before that 5 seconds up there is no change to the clock. If you take long then you will use some time off the clock.
A nice thing about simple delay is that the clock is monotonic. In Fischer and Bronstein the clock has count up after each move. A monotonic clock should make it fairly easy to add simple delay to an analog clock, for those who occasionally want to recapture some of that classic feel.
Get one of those $20-30 range analog quartz clocks that you can find at many chess and games retailers, e.g. [1]. I've never actually had a chance to look inside one but it is very likely to simply be two battery powered analog clock modules, with the switches simply toggling which clock is powered.
It should not be too hard to put an MCU in there like an ATTiny85 and have it monitor for clock presses. Put a transistor in series with each clock and controlled by the MCU so the MCU can delay the start of the clock.
You will want some way to change the delay time. Maybe add some buttons on back, but if you want to keep the hardware simple and you only support a small number of fixed delays you couple probably do something involving a pattern of button presses within a short time of powering on the clock.
[1] https://www.houseofstaunton.com/diamond-quartz-analog-chess-...
Sounds interesting, but as a player I think I'd prefer Fischer just so I don't have to think about the time so much (in delay if I play too quickly I "wasted" the extra).