I think lamp blinking varied by product. On cordless switchboards, IIRC there was 30, 60, and 120 flashes per minute. One meant incoming call, one meant ringing party, and one meant request for operator service. (I could look this up if desired). The 608 cord board had blinking supervisory signals.
IIRC some key systems had a double wink signal.
There may be signal for "camp on", that is a line waiting to be connected as soon as someone completes the call.
I think toward of the end of key systems, perhaps with Call Directors or the ComKey systems, there were more blinking options as they added service options. I used a ComKey but didn't care for it, modern or not. I don't like tone ringers and the loudspeaker intercom. I think ComKey was the last with a full thick cord with wires for each lamp and function; then they went to electronic sets.
I don't recall a flutter. However, our office had a tiny behive type lamp that lit steady when the shared line was in use. When the phone rang, the lamp fluttered. I think it was a neon bulb connected straight to the line without a relay (that employer was pretty cheap and would take only the cheapest solution).
Now the later generation "voice terminals" which had the red and green lights could do several things and the ringing signals could be programmed in all sorts of irritating ways. I would so much prefer a classic six button key set over them (Dimension? sets). Fortunately I have my plain old 2500 set, augmented by my 302 set*.
Upsets visiting high managers, but no one told me to remove it.