I've got a UITableViewCell that is in a TableView that is in editing mode. I have the cell's editing accent set to the Detail option. How can I access that little circle detail button that appears when my table view goes into editing mode, so that I can add a target to it?
You usually do not and should not access the accessory button of a table view cell.
When you want to invoke some code when the accessory button is tapped, you implement a method defined in UITableViewDelegate.
func tableView(UITableView, accessoryButtonTappedForRowWith: IndexPath)
func tableView(_ tableView: UITableView, accessoryButtonTappedForRowWith indexPath: IndexPath) {
//...
}