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Recently bought an R53 and I have been doing a lot of PM type stuff to it since I purchased. My TMAP sensor has something spliced into it and I haven't a clue what it is. No numbers or identifiable markings on it what so ever. I initially though it may be a HID box but nope...
I'm only guessing here ... BUT ... If that thing is tapped into your TMAP sensor (the one on your air intake) I would guess it is a "HooDoo" performance MOD. Again only a guess but it is basically a resister that makes your TMAP to think it is colder than it really is and this causes your ECM to inject more fuel vs air to increase performance.
BUT this only a Guess.
I would disconnect it and see if it makes any difference if your fuel mileage increases then the "HooDoo" magic performance MOD is what it is and you can live without it.