Ny wifes C3 had the same problem. Cant remember the codes off hand but dont recall it having P1631.
Took the motorised body apart and couldnt see anything wrong with it,pretty simples inside.
Car still randomly cut out/wouldnt rev after I put it back.
Got a genuine one from ECP and been OK for last year.
There is info in the archives here. Chaffed wiring loom across g/box was mentioned IIRCC.
HTH
Tony