We never have played them much. Back when the SEC only had 10 teams, they were not one of our five "permanent" opponents, so home-and-aways rotated among the other four teams (5 permanent, 1 rotating). We lost to them my freshman year, 1973, at home, on the famous UF QB David Bowden throwing it OB to stop the clock on 4th down play. With a week off, the most important thing to come out of that was Dickey starting Don Gaffney at QB against AU two weeks later. Gaffney was the first black QB @ UF, and he led us to the miracle win on the Plains (we have never beaten AU at AU prior to that) and the "November to Remember." Since we didn't play Ole Miss in '74, we must've played them at their place in '72.
When was the next time we played them? Sometime in the 80s. I know that they are the last team of any type (SEC, decent non-conf, or chump) to beat us in a home opener, and that was 1989 (yes, for some reason we opened with an SEC team that year).
So given all of that history, or lack thereof, who knows the last time they were favored over UF? Did we even play them when Archie Manning was QB? I know we lost to Eli in 2003 (I was there) at home - but were they favored in that one? Who knows? Maybe the answer is never?