Drain jar of maraschino cherries in a colander, then rinse thoroughly. Place on paper towels to drain off any excess moisture while you prepare cookie dough.
In a medium bowl, combine flour and baking soda and set aside.
In the bowl of your mixer, beat the butter, brown sugar, and white sugar on medium speed until smooth and fluffy, about 2 minutes. Beat in the instant pudding mix until blended. Mix in the eggs, one at a time, then mix in both extracts. With the mixer on low, slowly add the flour mixture until combined.
Finely chop drained maraschino cherries, and add to the dough. Add coconut and chocolate chips and fold until combined.
Using a medium cookie scoop (about 2 Tablespoons), drop dough onto ungreased cookie sheets, a few inches apart. Bake until edges are golden brown; about 10-12 minutes.
Remove and let cool on baking sheets for about 3 minutes, then remove with a spatula and place on cooling rack.