While crab cakes may sound like a budget-busting endeavor for a standard barbecue, they don't have to be. Crab comes in different grades usually labeled (in ascending order of quality) special, claw and lump. The texture of the lump meat is certainly lovely, but I like to reserve it for a simple presentation - like a crab salad, for instance - where its pricey texture can really shine. In this case, since we're mixing the crab with all sorts of other things and then frying it, reach for "special" grade - the flavor is the same. They won't, however, last very long. Get your "cook's-spoils" bites in early.
Return the pan to medium heat and add the celery, onion, corn and some salt and pepper. Cook the vegetables until beginning to soften, 3 to 4 minutes. Add the vinegar, sugar and pimientos to the pan and cook until the vinegar has reduced and the corn is tender, 3 to 4 minutes. Adjust the seasoning as needed and set the relish aside to cool.
Place a large skillet over medium heat with about 1 1/2 tablespoons of the reserved bacon fat. In a large bowl, mix together all of the ingredients for the crab cakes, along with the reserved crisp bacon, adjusting the seasoning as needed with salt and pepper. Working in batches as needed, scoop out about 1/4 cup of mix for each crab cake and cook in the bacon fat, turning once, until golden brown and heated through, about 3 minutes per side.
As batches finish cooking, reserve them on a plate; add more bacon fat to the pan as needed throughout cooking.
Serve the warm crab cakes over warm or room temperature relish.