If the Requirement isnt (as i initially assumed from the Original Post at
https://forum.krontech.ca/index.php?topic=730.0 ) to do this fully embedded Into an Single HDMI Connection, there turns out to be the Option to Trigger (at least the Blackmagic ones, have not checked for Atomos, see Page 9 of this PDF or the Attached Screenshot
https://www.bhphotovideo.com/lit_files/629692.pdf ) via a LANC Connector.
You can buy Record-Buttons for LANC-Connections fairly Cheap, and i assume those would contain some kind of Electronics and a Basic button.
Given that the Chronos Cameras also have an API, which would allow to either Start Playback via the API from an External Computer/ Device or at least get the Information, that the Camera is currently Starting or stopping the Playback of a Recording, it should be Possible to make a Small Box with some of those Single-Board-PCs or something like that.
Ideally the "Box" would connect to either USB or Ethernet on the Camera (Ethernet most likely will also need some kind of a Ethernet Switch to make a Working Network, USB should work without that, if its Possible to do via USB), and Listen for Start Playback, after which the "Box" would activate the Switch on the LANC-Button Thing (would need to be modified. Removing the Original Record Button from there, and wire that into some Output of the Small PC in the "Box") to start Recording on the Blackmagic Recorder.
If that is not Possible, The Computer would need to be Equipped with some Sort of Input Button (if there is no other way, a programmable single Key USB Keyboard with some Macro to run a Code would work too), to send a Start Replay Command to the Chronos, and that External Button would need to be used to Start and Stop the Replay on the Camera each time.
.
Now i am not a Programmer or know how to do any of those Fancy things with these Small Computer, but i attached a bunch of Screenshots from the API documentation along with the Path on where to find that (Camera needs to be connected to the Same Local Network as the PC, IP needs to be Set to Whatever your Cameras IP actually is, this is just Valid for mine at this current time; or just set a Static IP on yours).
Some People smarter than me in terms of coding will probably be able to make this a real thing, thats about all i can help here.
If you find nobody else, i guess clkdiv would have the Skills to pull that off. He made some Crazy rigs with Single-Board PCs, so if you cant find any other help here, he would be the Guy i would go ask (i can also call him and just ask, if needed. He probably doesnt follow whats happening on the Forum to closely, so he probably wont read this or the other Topic unless you or I link him that, so maybe try via PM on the Forum), if he isnt able to, he could at least tell you what to do or who else to ask.