I am just going off the NFL's definition:
"For the purposes of the Emergency Third Quarterback rule, a bona fide quarterback is defined as a player who wears a jersey number authorized for a quarterback and (a) is an established quarterback (e.g., someone who has customarily played the position in past professional or college seasons); or (b) is a player who takes regular-season snaps only at quarterback during at least three consecutive weeks of practice, including any week the player would be listed as an Emergency Third Quarterback."
Since Taysom wears number 7 and is arguably someone who has "customarily played the position in past professional or college seasons" I cannot assume that him being listed as a TE means that he is no longer considered a bona fide QB. It MIGHT mean that, but I need DA to answer that for us. I don't think the Saints listing him as a TE actually confirms that he no longer qualifies as a bona fide QB, especially since he definitely was a bona fide QB last season apparently.