The CA has no idle mode because it is already very low power.
How do you power the system on and off when you stop riding? If you wire the CA's power source to only supply Vbatt+ when the whole system is powered on, then you don't have to build a complicated automated switch.
Otherwise, you'll have to build a switch with a relay or transistor to disconnect Vbatt+ from the CA whenever it's not moving (what kind of sensor do you want to use for that? speedo? vibration? GPS?***) for however long.
If your system's throttle is provided by the CA, then this switch also has to detect that you've started moving again and re-power the CA, then you have to wait for the CA to boot up, and then your system will begin running again. Or you have to have a manual reset button, perhaps on the handlebars.
Note that your automated switch will continue to use power, so you'll want to design it to use as little as possible. The CA uses <100mA IIRC (you can measure your actual usage in your system to verify), so if your reason for the switch is to reduce power drain when not using the system, your switch will need to use less than the CA does, or else it will actually make the problem worse, assuming your reason for doing this is to decrease power usage.
***Whatever sensor is used by the automated switch will have to be powered by the switch itself, or not require any power from any source, so you can't use whatever sensor the CA uses if that sensor uses power, because it won't be operating when the CA is off, so it can't be used to reactivate the system after autoshutoff. If the sensors require anything ohter than battery voltage to operate, you'll also have to include a DC-DC to provide power to them, and that will use current all the time, so again, if this uses more power than the CA does, the problem is now worse....
