After a number of frustrating episodes for my wife and I, we came up with a plan. At my home office desk, I've got a 5x7 index card with a big red dot on one side and a big green dot on the other, which I use to communicate whether I'm interruptible. When green is showing, she's free to chime in about any random thing. When red is showing, it needs to be some kind of emergency. This has help us maintain domestic peace.
The shape and color of the dots borrowed from Brazilian steak houses where they have markers used to indicate whether the people serving various cuts of meat should stop by your table.
I made a home dashboard to display on the TV, which integrated with Toggl (time tracker extension) when my partner and I were living together: https://github.com/HartS/toggl-home-dashboard
Surprisingly, a feature to just "display a light when you're working" isn't super common.
Since it was just a keyboard shortcut to start the timer (I was also contracting at the time), this ensured my partner could see I was working easily without having to ask me :)
(apologies for poor code quality, this was hacked together extremely quickly... behind on tasks and needed a productivity boost, etc.)
The shape and color of the dots borrowed from Brazilian steak houses where they have markers used to indicate whether the people serving various cuts of meat should stop by your table.