not always???
Do you have an example exception?

Sure. You know where to find them.

???
Can you point the corresponding post Robert? As soon as you really named a local endgame then I do not remember a position for which the name of this local endgame does not indicate what is usually correct.

See [34]. https://www.lifein19x19.com/viewtopic.php?f=17&t=8765

"It can be correct to start locally with the gote option in a local sente (Example 7) or to start locally with the sente option in a local gote (Example 8). [...]"

I give you hints for reconstruction of a local position of my prominent shape class: Example 7 has T = T1 = 3.5. Example 8 has T = 5.5 and T1 = 4.

Of course, there is more fun, this time for one player's follow-up during the late endgame (my other example for the early endgame looks like one for the late endgame):

"Example 14 [...] A mandatory local start despite a high temperature T > F is unusual."

Hint for reconstruction: MSENTE = 10, follow-up move value F = 10.5.

As was just asking for a position not for a reference to books I do not have.

You are always just asking for a tiny bit more from the same sources, but there are limits to which I share of what took me three manyears to create. I do not copy and paste all of them. If you ignore the sources, reinvent the remaining parts by yourself!