Bugs in P2T2 probes.
We had an interesting problem on one of our 320's out here in SE Asia.
On the T/O roll, one engine wouldn't accelerate as quickly as the other, all accel checks couldn't fault the accel times, and all TSM procedures followed didn't help. The TO report from AIDS showed a difference in the T2 readings of a few degrees, but all wiring checks were OK.
What we found after a little suggestion from our IAE rep was to shove a very small boroscope up the back of the T2 sensing element chamber and look for obstructions. Found some leaf material in there. Cleaned this out and no further problems.
What we surmised is that this material blocks the airflow through the small cooling holes in the probe. When the P2 probe heater energises, this heat can now get transferred through to the T2 sensing elements because the cooling holes are now blocked, which then affects the fuel flow scheduling, thus accel problems. At the time, the TSM didn't cover this at all (not sure if it does even now).
An airline in China changed heaps of components for the same accel fault, only cured the fault after they changed the P2T2 probe by default (same T2 split)(surprise, surprise, surprise).
Hope this helps.