I take my daily L-carnitine during my feeding window at night.

There are different levels of fast, for most people most of the time (ie those looking for weight loss), taking a pill during the fast should be just fine (as long as you're under 30-50 calories).

That said, personally I do not like taking pills during my fast, as it will wake my stomach up and cause some hunger. Same thing with gum and stuff, but that's all individual preference :)