In reply to Thomas J. W.:
> Just wondering what people do in case they need both hands to fix something. I guess one can always tie it off ...
It would be simple to tie a knot but in practice a lot of people don't bother, and for good reason. The main danger of not holding the brake rope is of the grigri not locking up when loaded in a fall. This can happen in some circumstances, notably with a new, thin rope, a load which increases gradually rather than abruptly, and very little weight of rope below the device (e.g. when belaying from the ground). Once the grigri is already locked, this particular danger no longer exists. It then becomes a matter of making sure the device is not released accidentally, which would need either the lever to be snagged and pulled by some item of gear or clothing, or the weight released from the device and it not auto-locking again when reloaded. With a fair weight of rope below, this is highly unlikely, so many people will be happy sitting on a locked grigri without a backup while sorting out rope tangles and other issues.
Edit: To clarify that, when hanging on a locked grigri, it's far safer to keep it weighted and locked while you sort a problem out than unweighting it and perching on a small ledge, for reasons explained above.
Post edited at 08:20