I've no experience with the Jazz specifically, but I have replaced a few tailgates.
Usually, the best method is to remove the internal trims from both tailgates, then disconnect all the connectors and unclip and remove the wiring loom and washer pipe from the damaged tailgate, leaving it dangling from the back of the car. Once the old one is free to unbolt, swap the tailgates over - you will need an assistant. Then, use the chopped off loom as a guide to refit the loom from the car to the new tailgate, check that everything works, and replace the internal trim.
There may or may not be a connector in the rear body behind the trim, but if the loom on the new tailgate has been chopped, then the above is really the only option. There's not that much wiring to the tailgate, and as everything is on connectors, it's easier than it first appears.