I assume that you are referring to the chart in post 293 that asks "Where Is The Dollar-Deficit Relationship?". In fact, the possible relationships that I recall having heard of are visible in the following two graphs:
The actual numbers and sources are at http://home.att.net/~rdavis2/tradeall.html and http://home.att.net/~rdavis2/xchngmc.html.
The first relationship is between imports and recessions. As can be seen in the table at the first link above, imports decreased from 1974-75, 1981-82, 1990-91 and 2000-01. This was pretty much in the time periods of the last four recessions. The rationale that I've heard for this possible relationship is that consumers buy less of everything during a recession, including imports.
The second relationship is between exports and the trade-weight exchange rate of the dollar. As can be seen from the second graph above, the exchange rate generally went up from 1980-85, down from 1985-95, up from 1995-02, and down from 2002-05. As can be seen in the first graph above, exports generally moved in the opposite direction during this time. The rationale that I've heard for this possible relationship is that a weaker dollar makes exports relatively cheaper to foreigners who buy more of them in response.
Since the trade balance equals exports minus imports, decreased imports and increased exports will both tend to lessen a deficit or increase a surplus. However, the two possible relationships listed above show how just two factors can combine to effect the same item (the trade balance). There are likely many other factors that further complicate the study of any relationships.