Place Eggs In A Single Layer In A Large Saucepan; Add Enough Cold Water To Cover By 1 In. Cover And Bring To A Boil Over High Heat. Remove From The Heat; Cover And Let Stand For 15 Minutes. Place In Ice Water Until Completely Cooled. Gently Crack Eggs (Do Not Peel). In A Large Bowl, Combine 3 Cups Hot Water, Food Coloring And Vinegar. Add Eggs. (If Eggs Are Not Completely Covered By Colored Water, Add More Hot Water.) Let Stand For 30 Minutes. Remove Eggs With A Slotted Spoon; Peel. Cut Eggs In Half Widthwise. Place Yolks In A Small Bowl; Set Whites Aside. Mash Yolks With A Fork; Stir In The Mayonnaise, Onions, Cilantro And Mustard. To Level Egg White Halves, Cut A Small Slice From The Bottom Of Each; Place On A Serving Platter. Pipe Or Stuff Yolk Mixture Into Center Of Whites. Place An Olive Slice On Each; Fill Olives With Ketchup. Refrigerate Until Serving. This Recipe Is Best Eaten The Day It Is Prepared.