Is it a problem with the valve itself, or is it a related problem which sets this MIL flag

Could be either. Check to see if your car falls under the following extension of warranty:

http://www.epa.gov/compliance/resources/cases/civil/caa/toyota.html

Affected Auto list:
http://www.epa.gov/compliance/resources/cases/civil/caa/toyota_aff_veh.pdf

Could be either. Check to see if your car falls under the following extension of warranty:

http://www.epa.gov/compliance/resources/cases/civil/caa/toyota.html

Affected Auto list:
http://www.epa.gov/compliance/resources/cases/civil/caa/toyota_aff_veh.pdf

check : first - vapor pressure sensor(check the conector with engine on 4.5- 5 V, after pressure switching valve
the price for sensor - 180 -200 $ CAD
valve price is 124$
but, check the vacuum hose cracks, holed, blocked, or disconeced after you can change the sensor or valve
( I hade the same thing, i changed the sensor the light is gone,
after you chenge samthing you mast diconect the bateri