Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Confusion; Situational Awareness
Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Taxiway
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Airport
After landing at SJC (Runway 30L); we were instructed to exit the runway left on Taxiway J; and then to taxi; via V; to the [FBO] ramp.  I was in the left seat; the PIC was in the right seat with the airport diagram up in front of him.  It was dark; and I was taxiing the aircraft very slowly as I attempted to identify the correct taxiway.  I saw 2 taxiways; the first (parallel and closest to the runway) was clearly marked 'W.'  I looked -- but could not see any signage for the second/next taxiway (parallel to the runway and closest to the ramp).  I asked the PIC if he thought that was; in fact; Taxiway V.  He looked at the chart and affirmed that he thought it was. With both of us in agreement that we had reached Taxiway V; I turned left and began taxing to [FBO] (parallel to the [FBO] ramp).  A couple minutes later; Ground Control informed us that we had turned on to the wrong taxiway (that we were on Taxiway W1).  We were then given an additional instruction -- to turn right to enter the [FBO] ramp.  There was no traffic conflict or other issue.  The signage in that area of SJC is not adequate -- especially at night; and the airport diagram is a bit confusing as Taxiway V appears to be the taxiway on to which we turned. Suggest better (additional) signage on Taxiway J --clearly delineating taxiways W; W1 and V (especially important for night operations).
Medium Transport aircraft First Officer reported a taxiway incursion at SJC airport.  First Officer stated Taxiway J signage for taxiways W1 and V are inadequate at night.