In a medium bowl, whisk together the eggs, mayonnaise, chives, lemon juice, thyme, and cayenne pepper until smooth.
Gently fold in the crabmeat, trying not to break it up too much, maintaining the texture of the crab.
Gradually mix in the cracker crumbs until the mixture just holds together and is moist enough to form into patties.
Shape the mixture into eight equal patties, each about 3/4 inch thick.
Melt 1 tablespoon of butter in a large skillet over medium heat. Cook four crab cakes at a time until golden brown on both sides, about 6-8 minutes per side.
Remove the cooked crab cakes and repeat with the remaining butter and crab cakes.
Serve warm with lemon wedges or a spicy remoulade sauce.
Notes
To make this recipe gluten-free, use gluten-free crackers or breadcrumbs. Ensure all other ingredients, like condiments, are also gluten-free if necessary.