Navion ceiling adhesive pattern

Haven't experienced this personally, but did a little Googling. Since you mentioned the AC vents, could it be a result of thermophoresis, rather than the adhesive showing through, or (shudder) a hidden leak?

Thermophoresis–Soot deposits will often form patterns that correspond to the framing in
walls and ceilings, or will accumulate near sites of air movement, such as around HVAC
registers. The formation of such patterns is driven by temperature differences, and is
called “thermophoresis.” Suspended particles such as soot will move "down" a
temperature gradient. A temperature gradient is a declining temperature in one direction
through the air. A temperature gradient will occur across the surface of walls, where the wall area over the more thermally conductive framing is typically slightly cooler, during
cold weather, than the surrounding wall. It will also occur between the warm air leaving
a heating system register and the cooler wall nearby.. . .

From this link.

This causes the "filtration lines" or "filtration soiling", in the lingo of professional carpet cleaners, that frequently occur on carpeted surfaces along baseboards and under infrequently used doors etc. It can be called "ghosting" if it occurs on home walls and ceilings, where the structural elements become apparent. It is apparently quite difficult to clean.