From 2014 Owners Manual, page 19 of Foreword
From 2014.5 Owners Manual, page 21 of Foreword
Noise from under vehicle after turning off the engine
Approximately five hours after the engine is turned off, you may hear sound
coming from under the vehicle for several minutes. This is the sound of a fuel
evaporation leakage check and, it does not indicate a malfunction.
From the internet:
The key-off vacuum pump design is Toyota 's latest evaporative emissions system. As its name suggests, it has a vacuum pump that automatically leak-checks the evap system after the vehicle has been shut off.
First, the key-off system performs a leak check when the ignition switch is off. Second, a small vacuum pump (under trunk) creates the vacuum for this leak check. Depending on fuel tank size and fuel level, the vacuum pump usually runs 5 to 10 minutes or less during this test. And yes, the driver can hear the vacuum pump running.
For instance, the typical enabling criteria for a key-off system leak check are:
(a) the engine has been shut off for five hours
(b) the ignition switch is off
(c) engine coolant is 40° to 95°F
(d) intake air is 40° to 95°F
(e) altitude is less than 8000 ft.
(f) battery voltage is 10.50 volts or greater
Toyota has taken two steps to tell the customer that pump operation and therefore pump noise is normal. First, it hangs a warning tag on the shift lever (although no one can be sure how many of the warning tags survive the pre-delivery vehicle inspection). Also, a notice is printed in the owner's manual (that old-fashioned, print-media object hidden inside the glove box).