If you google the type of plug you have, you'll find a wiring diagram. Measure the resistance between each connected pin and the earth return pin. Anything that isn't open circuit or a straight short is probably fine, I can't remember if the rear & stop lights have a pin for each side, if not, check each bulb to be sure. Almost all problems are to be found in the plug, in my experience.
You'll find a cold brake light circuit hard to tell from a short with a lot of multimeters. The two brake lights share a common pin on the 7 pin plug.
If you can see continuity <100 ohms, between all the pins apart from the possibly unused fog light, you are most of the way there.
Rather than a multimeter, would it not be more straightforward just to poke 12v (scrap of wire from the OP's car battery if no other source available) down the relevant pins and see if the lights light up?