You should be able to get a timer from any hardware store, most commonly it's a dial with two pegs, one you set at the time you'd like the lights to come on, another you set at the time you want the lights to go off. Simply set the dial to the correct time of day, and voila, no more dark, lonely weekends for the Damsels.
Also, the lighting in that 12g might not be enough to keep an anemone healthy, most species require a high intensity light. What type of lighting do you currently have, and do you know specifically what kind of anemone it is? "Pink tip" could be several different species, and a picture would sure be helpful in IDing for you.
As for feeding, there are several different things you can try to see if your anemone likes them, a lot of people use krill and silversides, but i've even heard of people feeding squid and scallops. I wouldn't worry about not being able to feed it over the weekend, though, as anemones don't really need to eat every day. Two to three times a week, depending on how healthy it is (which we'd be able to determine to some extent if you get around to posting that picture

) is usually plenty.