The error disappeared.
But finally, I concluded that this GUI doesn't expose the button to UIAutomation.

I don't know why it appears on %ProgramFiles(x86)%\Windows Kits\10\bin\10.0.18362.0\x86\inspect.exe. There might be any other ways to find it in C#.  
For this specific GUI, I will take legacy, coordinate based approach using twapi.


```
eagle {
	set bool(true) [object invoke -create System.Boolean Parse true]
	set prop(invoke) [object invoke AutomationElement IsInvokePatternAvailableProperty]
	set cond(invoke) [object create PropertyCondition $prop(invoke) $bool(true)]
	set elems(invoke) [$elem(elan) -alias FindAll Descendants $cond(invoke)]
	$elems(invoke) Count
}
# => 0
```

Thank you very much for your advice.  
It will help me automate modern GUIs in future.