Up/Down goes ~” phrases

Up and down are adverbs. If an adverb (or adjective) fronts a clause, historically, this was followed by inversion: "Dearly do I love thee." "Bravely spoke he." ("Long was the road.")

In broad terms, other than as a poetic or literary device, this convention is now only used with locative adverbs and adverbial phrases: "Here is the key and there is the door" "In this house lived Sir John Smith." "To the west lies the river and to the east, the mountains."