The AF Mode (One Shot AF, AI Focus AF, or AI Servo AF) can only be selected in the P, Tv, Av, M, or B exposure modes. In the CA, and Auto (green box) exposure modes the camera sets the AF Mode to AI Focus AF and the option will not be changeable by the user. It should still show up on the camera's top LCD as the selected option when the AF-Drive button is pressed and an AF lens set to AF via the AF/MF switch on the lens is attached to the camera, though. Note that only some of the the Drive Modes (Single, Continuous, or the 10-second Self-timer choices) are selectable in the Auto exposure mode. In CA exposure mode only Single and the 10-second Self-timer are available.
If a lens is not attached to the camera, a manual focus only lens is attached to the camera, or an attached AF capable lens is set to MF (manual focus) via the switch on the lens then nothing will appear in the area of the top LCD for AF Mode, but the Drive mode options should still appear.
Is it possible to select AF mode through menu instead AF-Drive button?
Yes, it is possible to set the AF mode via the Quick Control screen (QCS) on the camera's rear LCD.
Page 38 of the EOS 5D Mark II Instruction Manual indicates that the QCS can be accessed by pressing the eight-way multi-controller joystick straight in. However, if you have C.Fn III -3:AF Point selection method (Please see page 198 of the Instruction Manual) set to [1.Multi-controller Direct] the QCS will not be displayed. (That is the setting I have selected for C.Fn III-3)
To get to the Quick Control screen I have Custom Function C.Fn IV: Operation/Others -3: Assign SET button (Please see page 202 of the Instruction Manual) set to 5:Quick Control screen. When the camera is in shooting condition (a half press of the shutter button will get out of any menus you may be in) pressing the SET button shows the Quick Control screen on the rear LCD. Use the eight-way multi-controller joystick to navigate around the screen until the AF mode is highlighted. When the AF Mode box is highlighted moving either control dial (the Main dial is directly behind the shutter button, the Quick Control dial is the large round wheel on the back of the camera) will change the selected AF Mode. Half pressing the shutter button to return the camera to shooting condition will preserve whatever AF Mode is displayed at the time.
When in the QCS you can also press the Set button again and see a screen with all three options listed. Highlight the option you wish to select and press Set again to choose it.