Keeping in mind that water can travel a long distance before it makes an appearance, what are the conditions immediately on the exterior of the home where the moisture shows up?

Post some images.

Are there openings, doorways, windows, roof valleys? Is the house one or two stories tall?

I think it's inevitable that you are going to have to open the walls on the interior adjacent to the problem area because if the moisture comes back again and again, it might be safe to assume that mold could be taking hold in the wall cavity where there should be insulation.

Dissolved minerals in water penetrate the home, then the water evaporates, leaving behind the minerals. Water can wick a long way. Check your gutters, downspouts, and grading a the first source of water infiltration. Then check to see if you have enough roof overhang or if you have brick touching the soil, ec.

A young-ish house built in 1985 in the U.S. would most likely be a brick veneer. So the description of the efflorescence on the inside, which would be drywall, is unclear.

Much more info would be needed.