Then why disappearing for weeks? If Jaime were dead, Cersei would know, and not only in her "guts" as her twin but the news would spread across the Seven Kingdoms, raven-post or not. If Brienne were dead to save Podrick or Jaime or both, then we'd know: what reason would have Jaime to remain hidden? Looking for Sansa on his own? Since he has no clue where she is, he'd have to ask questions. Sooner or later a man with a golden hand travelling with a squire (instead of a 6.5 feet wench) would be noticed. If both are conspiring to get the BWB on the other hand, preparation plans are required and perhaps some caution. I have this feeling that they are preparing to attack.