How did a Separatist tactical droid come into the picture in the Rebels' search for Captain Rex?

Question

In the new Ahsoka novel, we know that

Ahsoka was appointed by the Republic to lead Captain Rex and a detachment of the 501st to capture Darth Maul at Mandalore. They almost succeeded when Order 66 came down from Coruscant. Rex, who removed his control chip, managed to fake his and Ahsoka's deaths, who subsequently separated and went into hiding.

Years later, Ahsoka is a Rebel operative and suggested to seek out Captain Rex, who possessed extensive knowledge of the Outer Rim which would help the Rebels find safe havens to build a hidden base of operations at.

However, the two have lost contact with each other for years, although Ahsoka managed to somehow obtain a Separatist tactical droid's head which contained Rex's location (while Rex somehow managed to find an AT-TE to live in).

All Separatist droids were deactivated by Darth Vader and/or Sidious at the end of the Clone Wars, save for a select few types which were used by the Galactic Empire to police former Separatist worlds. Tactical droids are most certainly not one of these exceptions.

So, how did a Clone Wars-era tactical droid managed to contain Rex's Imperial-era whereabouts, and how did Ahsoka managed to obtain such a droid?

Answer 1

It’s not really clear

The show seems to imply that the droid did not contain Rex’s location. Rather, it was useful in tracking him down, due to its calculational abilities. From "The Lost Commanders":

AHSOKA: These droids were great at finding things, calculating. Found my master and I a few times when we didn’t want to be found.

EZRA: How in all the galaxy is that droid gonna find your friend?

AHSOKA: Well, I heard he was last seen in the Seelos system. You can start there.

If the droid had contained Rex’s location, Ahsoka would not have said he had "last been seen" in the Seelos system." It also would not likely have been scanning for a signal, as mentioned below.

Presumably the droid has a variety of ways of finding things (thus Ahsoka’s confidence that, given the right general planet, it could track down the clones). What’s not so clear, though, is what it’s using in the episode.

The droid appears to have been to be searching for a signal:

SABINE: Well, let’s fire this thing up. I think it’s scanning for a signal of some kind.

When the droid narrows down the signal, it says Rex’s number, 7567. It thus must have some way of identifying the signal as coming from him, specifically. It’s hard to say how this could be. One might imagine that the clones have some sort of tracker in them, but Rex already removed his chip, which was never described as containing a tracker in any case. Besides, if it could track clones, why would it only say Rex’s number, rather than that of the other clones? Perhaps it’s tracking the AT-AT, which is registered as belonging to clone trooper 7567.

What’s even harder to explain is how, immediately upon booting up, it seems to know to look for Rex. Perhaps it just was programmed to search for and identify clones or enemies generally?

With respect to these questions, neither the episode itself, nor Ahsoka, nor the “Rebels Recon” series of behind-the-scenes videos seems to say for sure.