A CL65 Captain deviated from his cleared taxi route at JFK; due in large part to the night time environment and poor lighting and signage.

Narrative

I was given a taxi route of cross 31R join C to runway 22R... I had never been given that route and also; usually they say turn on A or B and what direction. I was departing out of W; but I wasn't sure what the controller meant; but I had taxied in JFK I knew how to get where I was going. I ended up missing the last turn toward the runway even though it was a straight shot and I do not know how that happened. I somehow got on E and went around the back way to 22R (its kind of like V in ATL) and the controller saw my route and said that I could just keep going on E and make the right onto Y and then right on FB. When I got to the E and Y right turn; I almost missed it because there is literally no taxiway lights and JFK is notorious for poor signage; again I knew where I was going; but it just didn't happen. There were no conflicts; but I was upset because I had been to JKF many many times; but that night it was a little different since the flight had been delayed several hours and it was in the middle of the night in addition to the poor signage and lighting.