What was found
LOW FUEL PRESSURE LIGHT ILLUMINATED IN FLIGHT DURING DESCENT. PER QRH, TURNED BOOST PUMPS TO ON AND CONTINUED DESCENT TRYING TO GET TO WARMER AIR. LOW PRESSURE LIGHT TURNED OFF. GIVEN ALTITUDE AND PROXIMITY TO DESTINATION, CONTINUED AS THIS WAS ALREADY ROUGHLY COINCIDING WITH OUR CURRENT DESCENT, AND ESSENTIALLY THE MOST DESIRABLE AIRPORT GIVEN CONDITIONS. AFTER A FEW MORE MINUTES NOTICED FUEL IMBALANCE BUILDING. ATTEMPTED TO BALANCE BY RETURNING RIGHT PUMP TO AUTO , LOW PRESSURE LIGHT RETURNED, TURNED RIGHT PUMP BACK ON . AFTER REACHING WARMER AIR, ATTEMPTED TO BALANCE ONCE MORE, LOW PRESSURE LIGHT RETURNED AGAIN, RIGHT PUMP BACK ON ONCE MORE. FUEL IMBALANCE CONTINUED TO GROW, AND ALARMINGLY THE RATE OF GROWTH OF IMBALANCE SEEMED TO BE INCREASING. ELECTED TO SWITCH FROM THE EXPECTED INSTRUMENT APPROACH TO ANOTHER APPROACH WHERE WE WERE ALREADY CLOSER TO THE FINAL COURSE AND THEN CIRCLE TO THE NECESSARY RUNWAY DUE TO STRONG SURFACE WINDS, TO GET US IN VICINITY OF AIRPORT SOONER VS TAKING MORE TIME BEING VECTORED ALL THE WAY AROUND TO OPPOSITE SIDE FROM OUR ARRIVAL. AS SUGGESTED, A FASTER THAN NORMAL APPROACH AND LANDING SPEED WAS USED TO RETAIN ROLL AUTHORITY, AND CORRESPONDINGLY I ELECTED TO CONDUCT A NO-FLAP LANDING. IMBALANCE BY THE TIME OF TOUCHDOWN HAD GROWN VERY EXCESSIVE, AND CONTROL FROM ROLLING OUT ON FINAL ALL THE WAY TO TOUCHDOWN WAS PROGRESSIVELY MORE DIFFICULT, BUT ACCOMPLISHED WITHOUT INCIDENT. AFTER LANDING I ONCE AGAIN TRIED TO TEST BALANCING THE FUEL DURING THE TAXI, AND THE LOW PRESSURE LIGHT DID NOT RETURN, BUT NOTED THERE WAS NO RESOLUTION OF THE IMBALANCE PROBLEM - WHICH I BELIEVE CONTINUED TO GROW WHILE TAXIING IN. AFTER SHUT DOWN, THE FUEL FILTER BYPASS INDICATOR DID NOT APPEAR TO HAVE BEEN TRIPPED. UPON TESTING THE BOOST PUMPS, IT WAS DISCOVERED THAT THE LEFT PUMP INDICATOR ON THE CAWS PANEL DID LIGHT UP, BUT NO OPERATION OF THE LEFT PUMP.