Say we have a civilization on the verge of becoming Type II, and are in the process of building a Dyson Sphere. They are aware that in the process, and especially after completion, there will be telltale signatures of this construction process to anyone observing the stars in their general vicinity, such as abnormal dimming and possibly what appears to be its total extinguishing after the sphere is up.
That in itself may still not be a full giveaway as unless any observer is sufficiently advanced in their understanding of all stellar phenomena, they should be unable to completely rule out natural bodies obscuring the star intermittently. However, if coupled with the telltale structure electromagnetic waves take when used as a communications medium, it may point out quite clearly that intelligent activity is occurring in the vicinity of the dimming star.
Assume the observers are equivalent in scientific understanding and technology to modern humans. Is there a way for the civilization to communicate without the observers realizing that the dimming star is not a natural phenomenon? For the purposes of this question assume
The observers are already aware of the intermittent dimming of the distant star (approx 1400 light years away)
The observers are actively trying to determine if intelligent life is behind the dimming by listening for telltale radio signatures
The civilization will be considered to have successfully evaded detection if one of the following is achieved
They have a method of communication that cannot be detected at such large distances
They manage to mask their communication by disguising the emissions to look like emissions of natural bodies (real or theoretical such as quasars, pulsars, exotic stars and any other -ars you can think of)
As an aside, I know of Tabby's Star and that's exactly what inspired this question. I'm also aware that there is no stealth in space, so I'm not exactly banking on scenario 1 but who knows.