Air carrier Captain reported poor taxiway lighting and signage at ZSPD Airport made it difficult to identify the taxiways and the flight crew deviated from ATC's instructions as a result. The night time lighting conditions along with the rain were also contributing factors that added to the difficulty.

Narrative

We were given instructions to taxi south on B and hold short T2. Then we were told to hold short of V1 on T2. Shortly after we were given another frequency and as we were checking in I noticed I had passed Taxiway T2 and just approaching T1. I stopped the aircraft and told the First Officer (FO) to report our position and mistake. Before we could report this the Ground Controller asked what were our instructions at which point the FO tried to explain. We were asked to hold for a minute and then told to continue to taxi on Taxiway T1 to E and then continued to the runway without further issue or comment from the Tower. Possible contributing factors were night time; rain; and overall taxiway lighting and signage. With that being said it was harder to clearly view taxiways L19; T1; and T2 and being able to identify clearly taxiways with rain present and the lack of centerline lighting for 3 separate taxiways in a confined location. I see the need for extra vigilance and reduced taxi speed at this particular spot which happens to be a hot spot but for other reasons. Now there is an added risk of poor lighting - might be in repair - where it makes it harder to differentiate taxiways L19; T1; and T2. I will be much more careful in this area of the field in the future for sure.