Fiat stilo 1.2 16v 2004, revs keep hanging between gears, taking a few seconds to drop to idle, any ideas??

Yes, it is a known issue

https://www.google.com/search?q=vw+jetta+2.0+tfsi+rev+hanging

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https://www.fiatforum.com/stilo/125372-stilo-loose-connection-p1688.html

i have already answered it....there are cables connected outside with sensor....

Fiat dealer might be able to get it from serial number! Otherwise take to car audio specialist they can read the code from the memory chip!

Most likely not a wire, bad sending unit on the fuel pump, but most grounds are black or white/black stripe

JUST TAKE A JUMPER CABLE FROM BATT EARTH TO GEARBOX AND SEE IF IT IS THE PROB

the relay has blown & will need to be replaced

Your idle air controller (IAC) is hanging up and it needs to be removed and cleaned-remove the throttle body and clean everything, it makes taking the IAC out to clean much easier. IF you don't have a check engine light, you will soon. Cleaning the throttle body, the IAC and checking the throttle position sensor is very easy to do on these engines, I have one with 178,000 miles on it.

It could be tranny fluid, or your tranny may be screwed
change the fluid and filter and see what that does.

thanks.