Check in Tools-->Preferences-->Code Editor-->Caret Behavior
See if Enable Caret Blinking is enabled.
it's a known issue with several linux variants, search the forums for a few workarounds
I checked and it's Enabled, but this doesn't help unfortunately.
Thanks for your answer.
I checked for workarounds and still testing one of them: I changed the caret shape to "Quad Width Vertical Bar".
Also I tried to change its color but SQL Developer chooses almost random caret color instead of the specified one.
So it seems something is broken in caret display logic.