Get it doubled checked that it is actually a fuel pump fault.
My daughters RAv4 was mis-diagnosed previously and it turned out to be
the idle speed control valve, or the the idle air control valve, an old Toyota hand said its a common enough problem.
The valve is at the bottom of the throttle body, the fix is to remove the throttle body then remove the ISC valve then clean it thoroughly. Any half decent mechanic will do it
The valve may become sticky with carbon deposits, at the same time get the throttle body bore cleaned out with a brush and cleaner and it will fix the problem.