The system seems to be set up for more of an automatic operation, via the three position switch. I can't answer your question specifically, maybe this paragraph will help you come up with the answer.
(4) Fuel crossfeed switch. The fuel crossfeed valve is controlled by a 3-position switch, located on the fuel
management panel, placarded CROSSFEED - OFF. Under normal flight conditions the switch is left in the OFF
position. During single engine operation, it may become necessary to supply fuel to the operative engine from
the fuel system on the opposite side. The crossfeed system is placarded for fuel selection with a simplified
diagram on the overhead fuel control panel. Place the standby fuel pump switches in the off position when
crossfeeding. A lever lock switch, placarded CROSSFEED, is moved from the center OFF position to the left or
to the right, depending on direction of fuel flow. This opens the crossfeed valve and energizes the standby pump
on the side from which crossfeed is desired. During crossfeed operation, auxiliary tank fuel will not crossfeed if
the FUEL FIREWALL valve is closed. When the crossfeed mode is energized, a green FUEL CROSSFEED
light on the caution/advisory panel will illuminate. The crossfeed valve is protected by a 5-ampere circuit
breaker placarded CROSSFEED VALVE located on the overhead circuit breaker panel
Apparently the STBY pumps in conjunction with the CROSSFEED switch only work when in the OFF position, let me know what you think.
King Air 200, great airplane!