According to the owners manual of my 2000 LX470, the CDL is fully controlled by the button on the dash:
(b) Shifting procedure
To shift between unlock and lock modes in ”H”, push
the center differential lock button.
To shift between unlock and lock modes in ”L”, push
the center differential lock button.
To shift between ”H” and ”L”, stop the vehicle, put the
transmission into ”N” and move the four–wheel drive
control lever.
”H” (high speed position, center differential unlocked):
Lever at ”H”, center differential lock button left out
Use this for normal driving on all types of roads, from dry
hard–surfaced roads to wet, icy or snow–covered roads.
This position gives greater economy, quietest ride, least
wear and better vehicle control.
”H” (high speed position, center differential locked):
Lever at ”H”, center differential lock button pushed in
Use this for greater traction when you experience a loss
of power, such as wheel slipping, in the center
differential unlock mode.
”L” (low speed position, center differential unlocked):
Lever at ”L”, center differential lock button left out.
Use this for maximum power and traction. Use this for
climbing or descending steep hills, off–road driving, and
hard pulling in sand or mud.
In this mode, the braking feeling that occurs when the
wheels are negotiating a sharp corner is further reduced
than in the “L” (low position, center differential locked)
mode.
“L” (low speed position, center differential locked):
Lever at “L”, center differential lock button pushed in
Use this for maximum power and traction. Use this for
hard pulling in situations the vehicle cannot negotiate
even in the “L” (low speed position, center differential
unlocked) mode. Also, using this mode when driving
down steep off–road inclines will help contribute to
increased vehicle stability.