to interact in various ways — such as to participate, involve, interest, or attract
The exact meaning of this sense of engage depends upon its context. For example:
"They engaged in debate." — participated
"She engaged him in conversation." — involved
"She is an engaging conversationalist." — interesting
"She has an engaging smile." — attractive (attracting interest and interaction)
"The proposal engages the interest of many young voters." — attracts and involves
"She engages with her constituents." — interacts in a meaningful way
Sacks and boxes were piled high waiting to be delivered to the ships that sailed the Sea of Knowledge, and off to one side a group of minstrels sang songs to the delight of those either too young or too old to engage in trade.
engage = get involved
There are no more uses of "engage" in The Phantom Tollbooth.