IMO the interface should not be cluttered with unnecessary information, so my question is: What information is desired? Is it relevant to show the connection status all the time or perhaps only when the user is "asking"?
For example, even a permanent color dot draws attention. One that switches colors even more so. Traffic lights are for looking actively at, but I our case here is not (I assume).
If (if!) it is not desired to see the activity all the time, maybe it could show when you hover some place? ...or, if it affects when you should click Save, maybe it could appear as an infopopup when hovering Save. Or, if it is only a problem if it is Offline AND during Save, then the info comes up only then.
Also, I would guess that different icons but all in same size/color/weight, are less attention drawing than different color spots. I mean if you want something slightly subtler than colors.
<:-)