Scotch tape isn’t Scotch, and for that matter, neither are Scotch eggs. It’s probably just a misspelling that got carried forward and capitalized.
As the Edinburgh Tourist reports, “A traditional Scotch Egg is a boiled egg coated in pork sausage meat, with an outer crust of breadcrumbs. The deep-fried snack is called a Scotch Egg because the process of mincing the meat to go around the egg is known as scorching,” which is close enough to the word “Scotch” to cause confusion.
Similarly, per Etymology Online, using the term “Scotch” to mean “to cut, score, gash, make an incision” is an uncommon but not unheard of use, and historically, probably just a misspelling of “scratch.”
