An artist's depiction of an Extended Unit Death
I don't know of elegant ways, however you can try this overflow:
Minimap FreezeThat doesn't freeze the unit dots.
You could spam burrowed, visible units under the trees, it might make it so you can't tell when other units moved there because the minimap is always displaying the dots for the burrowed units.
Yeah, this is really the most sure-fire way if it's an option. Here's some useful information that may help if you want to use the above strategy:
When two units are at the same location on the minimap (e.g., a Scourge above a Zergling), the minimap has to resolve it to only one color at that location, so it has a pecking order. It goes like so:
1. Current Player
2. Player 1
3. Player 2
4. Player 3
...
13. Player 12
This means if Player 3 and Player 5 had a unit at the same location, everyone would see Player 3's color (teal by default, except Player 3 who would see lime green) on the minimap
except Player 5, who would see Current Player's color (lime green).
Now, how is that useful? Well, simply put, if you covered the entire map with units owned by Player 1, everyone would see that color on the minimap unless they had a unit there. So if you set Player 1's color to black, the minimap would always be black for all players, except for where their own units are (similar to when you toggle viewing the terrain by hitting the tab key).
I used the above concept for a minimap stats section used by multiple players. On null tiles, Player 1 (black) was a computer with units that covered a bunch of "8" shapes (like a digital clock), and each player had their own set of units (initially owned by some different computer player). Since they didn't own any units, the minimap appeared to be black. But then I could give units in a "5" shape from Player 9 to Player 2, and suddenly, Player 2 would see a green "5" on the minimap. Since Player 1 takes priority over other players (excluding Current), the other players still don't see anything on their minimap.
Maybe I should make a Theories topic on the idea... But anyway, if you wanted to truly block out visibility of other players' units on the minimap, cover the area with visible units owned by Player 1 (and yes, it can be any color you like).