Noticing visitors to our galaxy
Prelude
Prelude TLDR; A fleet of ships is passing through our solar system, stopping off at particular stars and causing small dips in the light from stars.
This is related to a couple of other questions (and a little suspension of belief to make it fit the story I want). The other questions are refueling and detection.
So the idea is that explorers from another galaxy have sent a fleet of their ships into ours - the ships need to refuel regularly by collecting fusion fuels from red giants (I've decided the ships also use the light and heat from the stars so I can 'explain' using stars rather than gas giants for fuel).
The fleet$^{\dagger}$ obscures some of the light from a star as it collects the fuel, making a small dip in the intensity of the light we receive from that star. 758
Then it moves on, using up fuel to power cryo, travel, AI etc and then stopping to survey and refuel at the next red giant.
$^{\dagger}$ One big ship can have a large volume without presenting such a large area to block out light. As explained in this answer we need a large area...so I'm making it a fleet with a main mother ship rather than one big ship.
The situation to reality check
As the fleet pass through our galaxy they obscure very small amounts of light to the point where they're almost lost in the noise of solar flares, sun spots and general brightness changes (I'm going to say they orbit their chosen star fairly quickly so we can fold the data and get a better signal).
A scientist in my story has come across this unusual trend of a small but very regular dip which appears for a specific amount of time, then disappears and turns up in another system...this trend seems unnatural to our scientist but has been overlooked by others. For the sake of argument I'm going to say that, so far, the ship has passed three star systems in the hundred years of data our scientist has but if you think he needs more I can change this.
I want our scientist to decide this is a sign of intelligent life and track the path of their ship (joining up the dots of red giants) and send out a message to them by predicting where they will be when a message can get to them.
(I want this message to include information about the star system he thinks they'll be in and information about ours so they can find us...but that is just background and for another question).
So how realistic is it that he would be able to track their path? Does he have enough information about their movements to predict where they will be?
(I'm aware he will be long dead before the aliens reach us, I want to give humanity generations of expecting the Aliens before they actually arrive).
Edit: I was imagining slower than light travel between stars and the initial group of red giants being close to each other. 302