Was the engineer testing something?
Is radiation involved?
No.
No.
Did it matter whether he caught any fish?
Did it matter whether the cigarette was lit?
Was it to demonstrate that the engineer was okay? Like, hey, check out this astronaut who just got back from outer space; is he suffering in agony while aching for the sweet release of death? No, he’s catching fish with a smile on his face; he’ll fry ‘em up for dinner just as soon as he finishes enjoying that big fine cigar!
No. (But I love your scenario!)
No.
Hmm, good question. I would say probably no, but I’m less sure about this one than the fish.
Were these activities directly related to an engineering task?
If so, was he gathering data?
Were the activities indirectly related to his engineering work in some way?
Completely unrelated (as in, “Hey, we need someone to do these things because [reasons], and we have this engineer available, so might as well have him do them”)?
Is it relevant what kind of engineer he was? If yes, was he a…
civil engineer?
Mechanical engineer?
Electrical engineer?
Chemical engineer?
Aerospace engineer?
Bioengineer?
Process engineer?
Sanitation engineer?
Train driver?
Ooh, good questions!
No. No data-gathering involved.
Not really.
Yes.
Somewhat.
civil engineer?
Mechanical engineer?
Electrical engineer?
Chemical engineer?
Aerospace engineer?
Bioengineer?
Process engineer?
Sanitation engineer?
Train driver?
None of these, but “train driver” is closer to his actual job any of the others.
Is this something that was seen on cinema or TV?
Was he acting?
Or was he just doing those activities and it was covered by the media?
If the person in question had not been a smoker, would they have instead given him some other task to do? Would they instead have had someone else do the smoking? Would the whole scenario not have come up at all in that case?
I think not, but can’t absolutely swear it wasn’t.
Depends how broadly you define “acting.” He was not doing a stage / film / TV performance or anything similar, though.
Yes, correct.
I expect they would have told him to smoke anyway (although, as per AnaByrd’s earlier question, he might have been able to get away with using an unlit cigarette in that case). It would not have worked to give him an alternative task or have someone else do the smoking.
Was he playing out the part of a member of the public? (e.g. testing how a seat works when a user is sitting in it doing typical things)
No.
Was it subterfuge?
(I’m picturing some kind of covert-ops mission where military personnel will swim out from under a boat once they get close enough to the shore or to the enemy ship they’ll stick explosives to — and they figure that someone might spot the boat and need a little reassurance — and so they’ll have the one guy who stays on board make a big show of lounging around like a lazy fisherman, complete with a cigarette dangling out of his mouth. So: who’ll remain on board to put on a show? Is it Fit Guy #1, who excels at clandestine run-and-gun hijinks? Or is it Fit Guy #2, same story? Or is it Fat Guy, who has a ‘steer a vehicle from place to place’ skillset? )
Was he used as an actor in a public service announcement about forest fires, which could be caused by a smoker who’s careless with a cigarette butt?
Taking a cue from the previous answer “He was specifically directed to engage in those activities.”
Yes, I would characterize it as subterfuge.
No to this specific scenario, but you’re getting warmer.
No.
Was he impersonating someone specific?
‘German assassins are gunning for FDR!’
‘Who do we have that looks most like him?’
‘Uh, Eddie the Engineer.’
‘So give him a cigarette holder!’
‘What?’
‘He’ll lounge around at the lake, do some fishing.’
‘And when the assassins strike?’
‘Our men open fire! And maybe Eddie survives!’
YES!!!
No German assassins, but otherwise, this is close enough to the actual scenario that I think we can consider it solved.
The US hadn’t officially entered the war at that point, but FDR was off at a secret meeting with British / other Allied officials in Canada, while the cover story was that he was on vacation aboard the presidential yacht. The yacht’s engineer, who bore enough of a resemblance to FDR to pass for him at a distance, was tasked with impersonating him, including, yup, smoking cigarettes with his trademark holder 
Congratulations!
Emphasis added
I call puzzle foul.
I will try and do better…
