The Saudis had long backed and had long-standing connections with traditionalist forces in North Yemen. In the 1962-70 North Yemen Civil War (really a proxy war) they backed the Zaydi Shia Mutawakkilite Kingdom of Yemen against the Egyptian-backed Yemen Arab Republic. The death of Nasser in 1970 helped bring an end to the hottest phase of the Arab Cold War and Saudi Arabia recognized the victorious Yemen Arab Republic and worked in coordination with various factions in North Yemen, preferring it over the Marxist South.

Yemen's unification in 1990 came at a precarious time. The overall Cold War was ending with a Soviet collapse and Saddam Hussein's invasion of Kuwait threatened to rip apart the Middle East. The president of the newly re-united Yemen, Ali Abdullah Saleh, backed Saddam in sharp contrast to the rest of the Gulf States.

Partly as a result of that the GCC countries split from Saleh, and flirted with the secessionist movement in 1994. As it happened, the 1994 Civil War so brief that I'm not sure you should quite read into it the way the wording of your question suggests.

Saleh claimed US support but it wasn't a major break from the rest of the US' GCC partners.

Saleh won so quickly that the war couldn't become the kind of protracted proxy conflict that characterized the North Yemen Civil war decades prior, or for that matter that characterizes the conflict in Syria today.

The other motivating issue that remains relevant are accusations that Saudi Arabia is concerned about the potential power of a united Yemen on its southern border. The population of Yemen is at least equal to Saudi Arabia, and that's only if you believe the official Saudi population figures, which are dubious and likely inflated.

You're not likely to find much in the way of concrete discussion/documentation of any of these factors from Saudi officials, however. Saudi Arabia remains one of the most opaque polities in the world, these Carnegie Endowment articles would be a good overview though:

http://carnegie-mec.org/diwan/62405 http://carnegie-mec.org/diwan/60627