When the G1 X is set to Manual (M) mode, AEB no longer shows up in the FUNC menu. Is there another to set it? Seems like a serious limitation otherwise.
AEB (Auto Exposure Bracketing) lets you take a normally exposed image, an underexposed image, and an over exposed image.
When you are in aperture or shutter priority mode you are locking one of the variables that affects exposure and the camera controls the others. Normally the camera will adjust these settings to get the desired exposure.
If you go into manual mode then you are saying you want full control of all variables/settings so AEB won't work. The camera does not know which settings it can change to get the desired effect. If you have AEB functionality in manual mode then the camera should adjust the shutter speed to get the desired exposures.
If you cannot use AEB on your particular camera while in manual mode then you can get an intervalometer (or a smartphone app for DSLRs) and once you know your shutter speed for a normally exposed image (using a light meter like the one in your camera or a dedicated one) then some simple math gets the brackets you want.
On Canon cameras (and I would assume others, but I've only ever used Canon) you can define if a picture should be over/under/normally exposed when in aperture or shutter priority modes. AEB just lets you automatically take the same picture multiple times with different exposures and is no different than if you adjusted the exposure yourself between shots (except that it also reduces camera shake as you're not bumping the camera). There's nothing fancy about AEB.
That also happens in other Canon models. My guess is that when using AEB in other modes (P/A/S), the camera knows that you want one of the parameters (aperture or shutter speed) fixed, so AEB can use the other (and also ISO) to bracket correctly without interfering with your initial intention. As far as I could test, AEB on P mode also fixes the aperture, just as AEB in A mode.
If you need to bracket in M mode, choose which parameter is more important to you (aperture or shutter speed) and switch to the corresponding mode (A or S) to use AEB. OTOH, on the A and S modes you maybe limited in the range available for shutter speed, so long exposures won't be bracket.