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What was the original condition with the car? What lead to the ABS pump replacement?
OK your post said VSC light, you just said ABS light, just want to confirm which it is?
So the ABS light isn't on at all?, just the VSC comes on after you shift it into gear and start to drive correct?
After replacing the ABS pump was a zero point calibration done to the VSC system?
The zero point calibration is probably undone or not correct.
Visit this youtube video link, it shows how to manually do the zero point calibration with out a scan tool..... https://www.youtube.com/watch?v=55XmiSsGQgo
Do you have access to a scan tool?
No it can be checked in the park position, there are codes in the system that will relate to the VSC light. Most code readers will not see these codes,unless they are higher end scan tools. I really think that it is a zero point calibration issue, this is so common on these cars, especially when people replace the battery. If you do decide to take it to a Toyota Dealer I doubt they would charge you more then $100 to scan it and do the zero point calibration if it needs it.
(a) Clear the zero point calibration data.(1) Turn the ignition switch off.(2) Check that the steering wheel is centered.(3) Check that the shift lever is in P.(4) Turn the ignition switch to ON.(5) The ABS warning light and slip indicator light come on for 3 seconds to indicate that the initial check is completed.(6) Using SST, connect and disconnect terminals 12 (TS) and 4 (CG) of the DLC3 4 times or more within 8 seconds.(7) Check that the slip indicator light comes on.(b) Perform zero point calibration of the yaw rate and acceleration sensor.(1) Turn the ignition switch off.(2) Check that the steering wheel is centered.(3) Check that the shift lever is in P.NOTICE:* DTCs 36 (Zero Point Calibration of Yaw Rate Sensor Undone) and 39 (Zero Point Calibration of Acceleration Sensor Undone) are stored if the shift lever is not in P.* If a DTC is output that indicates zero point calibration is incomplete, repeat the procedure starting at the step for clearing the zero point calibration data and system information.(4) Using SST, connect terminals 12 (TS) and 4 (CG) of the DLC3.(5) Turn the ignition switch to ON.(6) Keep the vehicle stationary on a level surface for 5 seconds or more.(7) Check that the slip indicator light comes on for several seconds and then blink in the test mode pattern (0.125 seconds on and 0.125 seconds off).HINT:* If the slip indicator light does not blink, perform zero point calibration again.* The zero point calibration is performed only once after the system enters test mode.* Calibration cannot be performed again until the stored data is cleared.(8) Turn the ignition switch off and disconnect SST from the DLC3.(c) Drive the vehicle straight ahead at 40 km/h (25 mph) or more for at least 10 seconds.