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If you have 12v when you place the tester at the brake light bulb socket,I do not think it is a grounding problem. I would have to guess the problem is at the socket and your connection with the bulb.
Your problem has to be the socket contact for the brake light not touching the bulb contact if the bulbs you tried are good. Everything you have described eliminates the ground connection and the 12v. supply to the socket so it has to be the bulb is not contacting the socket contact.