Does this point to anything in particular as the source of the problem? Is this the kind of pattern you would expect if the lights were wired in series and there wasn't enough current?
Wired in series would have no effect unless there is a miss connection along the way. And again, all lights would blink if there is a short in a connection..
The only way to fix this is the structure must come apart. If you soak all of the structure joints with alcohol, several times. Then gently use a sharp xacto knife and scribe your way through the joints, it will come apart. Alcohol will soften the hot glue.. Then you can re-wire or install new LEDs. Or fix/adjust any broken connections or other problems you find'...
