While the Canon 6D battery life may be great for taking modelling photos, I've found that leaving the Canon 6D internal GPS on while the camera is switched off runs the battery dead within a few days. With GPS switched off while the camera is off the battery remains charged.
Unfortunately the only menu option on the 6D is to turn the internal GPS on or off, there is no choice to switch GPS off when the camera is switched off which would still allow GPS data to be added to photos taken. The option that you would expect to switch the GPS off when the camera is turned off is the "Use GPS to track camera". With this option off there seems no point in the GPS being permanently turned on.
You can tell if the GPS is switched on by looking at the top LCD plate of the Canon 6D when the camera is turned off. If the GPS is still active the screen will be showing GPS in the bottom corner. With GPS off this disapears.
Hopefully Canon will be able to resolve this with a firmware update so that you can retain GPS live only when the camera is on rather than GPS remaining live when the camera is off.