Preheat oven to 375°. Line a rimmed baking sheet with foil.
Place turkey, onion, and pineapple on prepared baking sheet. Drizzle with oil, and sprinkle with salt and ¼ teaspoon pepper.
Bake until a food thermometer inserted in thickest portion of turkey registers 165°, approximately 15 minutes. Let cool on a wire rack.
Transfer turkey to an airtight container, and refrigerate until ready to use.
Place onion, pineapple, relish, and remaining ¼ teaspoon pepper in a medium bowl. Using a hand blender, blend mixture until smooth. Transfer relish mixture to an airtight container, and refrigerate until ready to use.
Using 2 forks, shred turkey into large pieces.
Spread a layer of relish mixture onto bread slices. On 4 bread slices, layer watercress and turkey. Cover with remaining bread slices, relish side down.
Using a serrated bread knife in a gentle sawing motion, trim and discard crusts from bread. Cut each sandwich into 4 (3×1-inch) rectangles. Cover with a damp paper towel, place in an airtight container, and refrigerate until serving time.
Recipe by TeaTime Magazine at https://teatimemagazine.com/turkey-tea-sandwiches/