I have read but cannot find how to set the clock time and the clock show time even after we switch off engine. 
Hi Jazz,
Just to be sure, we are talking about JVC KW-XG506/KW-XG505.
Had done some checking.
Setting clockTurn the ignition switch to position Acc (2).
Follow instructions on pages 17-18 which shows how to set clock.
(Clock H = Hour adjustment and Clock M = Minute adjustment)
Clock displayYou can set the clock time to show on the display at all times when the power switch (on the SS unit) is turned off (the power switch is on the top left hand corner on the SS unit). However, the ignition switch
must be in position Acc (2), ie, the car's electrical system must be set to deliver power to electrical accessories.
When the ignition switch is set to off, the clock display will not show at all.
However, when you press the DISP button, it will show the clock time for about 5 seconds irregardless of whether the power switch (on the SS unit) is turned on or off.
Hope this helps ..........