
Long review ahead, so I've included a TL:DR section at the bottom. Feel free to skip to that!
Forensic kit is interesting in that, while you can use it to investigate with , realistically it's more specialized towards investigation with . The reason for this is that its extra horror-healing benefit only works with an exhausted enemy at your location, and while there are other means to evade/exhaust enemies (e.g. Transmogrify), 9 times out of 10 you're going to be using for evading as normal. If you want to investigate with then you're far better off using Grim Memoir, which has an identical resource cost and number of uses while offering a bigger skill boost and arguably a better benefit for most Seekers (the possibility of card draw).
Where this card starts to shine is on Rogues who can take it (in particular Kymani Jones, Trish Scarborough, Finn Edwards and potentially Monterey Jack) or Lucius Galloway as the one Seeker who is slightly more specialized towards (especially with his ability). All of these investigators have below average Sanity (and some like Lucius and Jack have weaknesses which deal you horror), so having an option with both gives you clues and heals horror linked to your preferred enemy management option (evading) is excellent card compression. It makes standalone solutions to these problems (e.g. Liquid Courage) much more questionable.
The obvious comparator to Forensic Kit for agility users is Thieves' Kit. Thieves' Kit by contrast has more uses, doesn't offer a +1 skill value, and returns resources for successful investigation. The uses here is a key consideration, as Thieves' Kit is okay for longer before you need to replace it. For me though, rather than considering these cards as competition, I'm very likely to take both on investigators where I want to use to clue-find (and if you have one in each hand, you can use whichever is more beneficial in the circumstances). Having four cards in a 33 card deck that allow for this gives an 81% draw chance of at least one in a hard mulligan, which allows your investigator to get clue-finding much more quickly without needing to fall-back on things like Streetwise.
For cards that interact well with Forensic Kit, there's String Along and "Where's the party?" - both of which keep enemies engaged with you after they become exhausted. This allows you to drag enemies to other locations with clues and so heal horror (and can help fire off abilities like Lucius’s, especially if you drag an enemy to a location with clues in preparation for it readying in the upkeep phase). Kicking the Hornet's Nest is also nice to spawn an enemy at a location with multiple clues (and so then evade and use the Kit). Alton O'Connell is worth a mention, as he boosts but also allows for occasional clue compression when succeeding by 1 or 3 (which I'd argue is more common on Rogues using to clue-find, as they don't have as trivial ways to boost agility compared to Seekers who have things like Magnifying Glass for intellect). Pilfer can be synergistic from having clue compression off , but whether the resource cost is worth the price of admission is up to you.
For a look at a deck in practice that uses Forensic Kit, I've just posted an Ascetic Kymani deck which uses both Forensic Kit, Thieves' Kit and Grappling Hook to have a lot of ways to clue-find with agility. Feel free to check it out!
TL:DR
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Forensic Kit favors investigation through , as Grim Memoir otherwise is typically superior for clue-finding with .
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High Rogues who can take it and Lucius Galloway are therefore a good fit, as they all have below average Sanity and can readily evade enemies to benefit from its horror healing.
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Thieves' Kit is an obvious comparator. Taking two copies of both Thieves' Kit and Forensic Kit can be beneficial, as it gives an 81% draw chance to find at least one in a hard mulligan on a standard deck.
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Cards which pair well are String Along and "Where's the party?", which keep exhausted enemies engaged with you for opportunities to heal horror even when changing locations. Kicking the Hornet's Nest allows you to spawn enemies on locations where there's already clues, evade them, and then use the Kit.
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Alton O'Connell, as a new level 0 booster who provides occasional clue compression, is also worthy of consideration. Events like Pilfer have overlap due to testing for clues.