I often hear people use the word spike w/r/t this kind of thing, but it seems to me that "spike" is used as an agile code word when speaking with stakeholders to conceal what is actually going on: good ol' fashioned _research_. There's nothing wrong with research or planning, but I've seen a lot of engineers who seemed constitutionally incapable of calling it this in front of stakeholders.
You mention defining when a spike is 'done', and timeboxing. I understand why we do this, but there are times where I believe it contradicts the very nature of doing adequate research. We have a known unknown, and so we do some research to make that unknown known. In the course of doing research though, you will discover there's a cascading set of new unknowns which must also be understood. So, identifying a 'done' state, depending on the nature of the research we're talking about, can be a totally fraught activity.
Kinda ranting here, but this is a common scenario: "Within the next week, we'll spike to get a more accurate estimate of the time it will take to build a cluster that meets the requirements we've agreed to, and propose several technical recommendations which will fit the budget." I've seen too many instances of this where 2 more days, another week, maybe a whole month could have been spent answering these questions _correctly_. Now sure, if you have a trusting relationship with your stakeholders, you can easily negotiate that you think a solid set of recommendations will take another week, but there is a certain amount of pressure to just be done with it and smile, and I've seen
this kind of thing backfire over and over again depending on the level of trust that's been established between product teams, stakeholders, and engineers. 3 months into the project, the realization settles in that the database you've chosen will not scale on writes the way you'd hoped it would. Now what?
I don't recall where this quote is from, so if someone knows the source please let me know: "Weeks of programming can save you hours of planning."