This is not a secret - Perry has publicly stated that the last Democrat for whom he voted in the general presidential election was Carter in 1976. Since he is the only one to know, I take his word over those who are just making assumptions, especially people who don't even know how politics worked in Texas in those days.
You have a point.
Anyone in Perry’s position who is willing to publicly admit to having once voted for Jimmy Carter is unlikely to be anything less than completely forthright regarding his subsequent votes.