The inner rubber boot with the side cable entry comes out with the connector. Grab the part of the boot that is around the body of the connector as close to the bulb as your fingers will allow, and pull firmly while walking it side to side. It might have some corrosion on the terminals that makes it hard to remove. Inspect it, and use a light coating of bulb grease or silicone grease when reinstalling it. Make sure the connector is pushed in all the way when reinstalling it. I just checked mine before I replied to your post, and it was about to fall off the bulb!