AN ACR MLG CREW TAXIED ONTO A SVC ROAD AT NIGHT IN THE RAIN.

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OPERATING JAX-LGA; AFTER LNDG ON RWY 22 AND EXITING THE RWY ON TAXIWAY C; WE INFORMED GND CTL THAT OUR GATE WAS OCCUPIED AND TWR CLRED US TO THE TAXIWAY ZA HOLD AREA. WE FOUND ZA ON THE COMMERCIAL CHART; HOWEVER UPON ARR AT THE INTXN OF THE INNER TAXIWAY AND TAXIWAY ZA; WE FOUND TAXIWAY ZA POORLY MARKED AND LIGHTED. THIS FACTOR PLUS THE RAIN MADE THE TAXIWAY ZA DIFFICULT TO SEE. I MADE THE INITIAL TURN ONTO TAXIWAY ZA PROPERLY. THE CHART SHOWED THAT TAXIWAY ZA WAS A LOOP OFF THE INNER. I KNEW THAT TAXIWAY ZA WOULD BEAR TO THE L; HOWEVER; I TURNED L TOO SOON AND ENDED UP ON THE SVC ROAD BTWN THE INNER AND TAXIWAY ZA. WHEN TURNING ONTO THE SVC ROAD; THERE WERE NO VEHICLES ON IT. HOWEVER; A SMALL TRUCK PULLING A BAGGAGE CART DID COME ALONG. I COULD NOT TURN OFF THE SVC ROAD; SO I SIGNALED THE TRUCK AROUND ME. THE TRUCK PASSED WELL CLR OF MY ACFT. THE CTLR INSTRUCTED ME TO TAXI AHEAD AND JOIN THE INNER AGAIN. I DID THIS WHILE A FUEL TRUCK WAITED AT THE INTXN FOR ME TO PASS. THERE WERE NO FURTHER PROBLEMS AND; AFTER BLOCKING IN AT THE GATE; I CALLED THE LGA FAA CTL TWR. THE SUPVR SAID THERE WAS NO PROBLEM IN WHAT HAD TAKEN PLACE AND AGREED THAT TAXIWAY ZA IS VERY POORLY MARKED AND LIGHTED. I WAS ALSO TOLD THAT THEY HAVE HAD MANY COMPLAINTS ABOUT TAXIWAY ZA. ALSO; THE ACR OPS SUPVR TOLD ME THAT WHAT I HAD DONE; HAD BEEN DONE BEFORE. IF THIS TAXIWAY IS TO BE USED IN THE FUTURE; IT NEEDS TO UPGRADED.