Went up and down with two Yankees carrying old dictionary (2-4)
I believe the answer is:
yo-yoed
'went up and down' is the definition.
(yo-yo can mean to move up and down)
'two yankees carrying old dictionary' is the wordplay.
'two yankees' means two replacements for 'yankee'.
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'carrying' says to put letters next to each other (in a down clue, the bottom letters carry others).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'dictionary' becomes 'OED' (Oxford English Dictionary).
'y' put after 'o' is 'oy'.
'y'+'oy'+'oed'='YO-YOED'
'with' is the link.
(Another definition for yo-yoed that I've seen is " Fluctuated rapidly".)