Usually you'd say "its tail wags" or some kind of noun+verb if ur doing 2 unconnected words...'all' is ur noun..."connected" is ur verb...all connected...tail wags...
tail-wags is different from tail wags....but "...its 'tail wags'..." can be the same as tail-wags.
all-connected vs all connected...same procedure. The dog's all connected. The world's all connected. The master's all connected. The chair's all connected. It doesn't really make sense unless u view it as: the dog's all-connected. or: the dog's 'all connected'. Adding quotes doesn't change the words it just changes the annotation...so that seems the most acceptable level of 'interpretation' like in the OP...since ur effectively just bolding or underlining a part of the '4 word' theme, so its meaning is emphasized 'somewhere' but ultimately unchanged.
Looking at the precedent of jam interpretation: the theme can be dumbed down to 'connect'/'connected'/'connection'....or whatever synonym/tense of those words u want. So if you do that u are going to be just as relevant as most of the other presumed interpretations....since the literal meaning is, again, fairly explicitly cryptic.