Revealing mistake: When Sallah rides up to the tank to help, just as Indy shouts, "Get Dad!" we can see that Henry is actually lying on protective support, and not lying directly on the moving tank treads. (01:35:40)
Continuity mistake: While Henry and Marcus are being held inside the tank, Indiana rides in circles and baits the tank to ram into one of the cars. In a following shot when we see Vogel walking toward the window inside the tank it's a flipped shot, note everything is backwards: strap, button, armband. Then two shots later, when Vogel shouts "quick" in German it's another flipped shot, and about five shots after that again flipped. (01:29:30)
Chosen answer: They're not, no. An individual doesn't become immortal after one drink - it requires them to drink regularly in order to remain alive. So neither Jones has been rendered immortal, merely healed of any wounds that they might have. But your surmise is basically correct - as the Grail cannot leave the shrine, any individual wishing to use it to prolong their life must stay there if they wish to enjoy its effects.
Tailkinker ★
Also, in Indiana Jones and the Kingdom of Crystal Skull, Henry Jones, Sr has passed away before the start of the story and therefore was not immortal.
raywest ★