Solution to "iPhone blinking in Finder"
A thread from 2020 addressed Finder's endless unsuccessful attempts to recognize an iPhone/iPad. it ended up with the recommendation to call Apple support.
https://discussions.apple.com/thread/251303972
There is a much better solution that works for many people in many different configurations of Mac OS and iOS.
See: https://macreports.com/iphone-keeps-connecting-and-disconnecting-from-mac-fix/
Short answer: open Application Monitor. Type "usbd" in the search field. End that process. That's all.
There's also a simple solution for those who prefer to use Terminal.