Stillwater [Okla.] Democrat (May 27, 1915), p. 4:

NEW VERSE TO "RYE STRAW."

Of all the fowls that roam the air
I had rather be a peckerwood;
I would fly upon some tall dead tree,
And there I would peck, and peck,
As long as the pecking was good.

Compare Gove County Leader (Gove City, Kans.) (July 16, 1897), p. 2:

“Yesterday a woodpecker flew and lit on the courthouse door, and he pecked and he pecked until – continued next week.”

The full version (not printed in the paper) is "till his pecker was sore."