high powerd squirt gun, just a suggestion, if you wait around maybe mrssittingduck will have an answer she seems to be a very informative bird lady. Just don't harm it, try some other means.
There are really only two reasons for woodpeckers to peck. One is to make a nesting location (is the bird brightly colored or plain) and the other more common reason is to find bugs to eat. What type of wood is your garage made out of and what condition is it in? The birds may be feeding on TERMITES!
Try one of the artificial owls or another type of preditor birds, this scared mine off for a while. Sometimes firecrackers will work, be careful and don't burn your garage down even though this would solve your woodpecker problem. Totally last resort, get a permit from proper people and tell the bird he or she has one more chance to move out or they will visit the ground gophers.
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