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The picture from the link is the Light Patrol Ship.
I'd be obliged if you'd say why you feel confident to state that categorically. There's no basis to do so on the evidence from the prime source.

Above is the complete relevant four page sequence that features the Light class. As you can see the Stats & Caps are terribly disjointed.
First we have the Law class, then the PB-950, Light Class, Light Corvette, Customs Frigate and the Guardian class. I've attached thumbnails of the Guardian and the Light Corvette to their relevant S&Cs. That leaves us with four ships, and three illustrations.
One might assume that the illustrations are at least in the same order as the S&Cs, but that can only be an assumption, WEG have not stuck with such a convention all the time.
There really is no way to determine how these pan out, but to me, the ship marked as B shows enough CEC design features to attribute it to the PB-950.
The ship marked as A fits the design styles of none of the ship builders subsequently listed, however, the weapons load out rules it out of contention for either the Customs Frigate or the Light class.
That leaves us with ship B being either the Customs Frigate or the Light class (green or gold). The S&Cs for green and gold describe very similar weapons systems, so that's no help. Moreover, it must be said, that B looks nothing like a normal SFS design - it has none of the grace and elegance typically associated with that manufacturer, and is missing the very large CRMS panels seen on every single SFS design to date. The only remaining factor that can be used is that B appears on the same page as the gold text, so it seems likely that the ship's illustration is of the Customs Frigate,
not the Light Class.
Now, it may or may not be the case that the ship shown in Brak is the same ship shown as B, and that Brak then goes on to state that this is the Light class, but even in this case, it would represent a WEG illustrator taking an off-cuff guess and/or simply applying standard writers practice and using a ship illustration that already exists rather than commission an entirely new design.
As such, without new evidence to hand, it is my opinion that the ship is most likely to be the Customs Frigate, and that WEG have simply glued the wrong S&C.
I'm quite happy, in theory, to work up the ship, though it would be as the frigate. Getting the Brak plans would be extremely helpful in doing so.