Do you think these jobs are so easy, intellectually speaking?
It's all relative and I am not familiar enough with these profession to make a judgment. At the task level, I'd say yes... but I don't know for sure and haven't read anything in particular to plumbing.
What if IQ tests were instead to "solve" a large number of crimes, or to fix a bunch of machinery? Would there be a corellation with Openness?
If you change the relationship, then no, there wouldn't be. I don't see the relevance, however. In both cases, higher IQ within the groups relate to better performance (crime solving and machinists both being tested before, FWIW). It'd just be a crappy IQ test (colinear with performance). In any case, it's just a matter of reference point.
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However, those are problems best left for their own thread. What I was referring to is the concept that IQ is part of personality/a subset of personality. Unlike N/S, the distribution for intelligence doesn't match the general population, meaning that if you model Ns IQ vs Ss IQ, the normal IQ curve is very very different with the peak below average, but a gigantic tail end into high-IQ areas.
IOW, Ss have an extreme range of intelligences while Ns have a very narrow range. As above, the reason why some mechanics will be better is
because IQ ability is not directly linked to personality. The relationship is complicated. Ns answer pretty directly "I am not a good mechanic"... but that doesn't mean that one can't be a good mechanic and have a high IQ. You inherently assume that Ss (ie: mechanics) will have lower IQs whereas Ss have a rather extreme range of available IQs, compared to Ns that bunch around 110. Instead of looking at intelligence for what it is we attempt to attack the concept, despite that it applies even within those sub-sets. Mechanics are not treated unfairly - the range of mechanic ability is gigantic, with high IQs at the top. Being "an S" doens't make one at the top, but neither does being an N. Testing different things. Personality needs to stay out of intelligence entirely.
The "mechanic" aptitude is spread along the Ss axis, IOW, ranging from sub 80 IQ to 120+IQ... in large numbers. Ns, however, are spread from the sub 100-120+ IQ... in a giant peak. But they make lousy mechanics. That makes the statement: Mechanics have lower IQs / IQ tests are unfair to mechanics technically correct. And yet, totally wrong. High IQ mechanics are those in mechanical engineering - a high IQ degree - or in a technical school, the mid-range IQ.
MBTI simply created an entire category for people to feel special in, what with all the veiled intellectualisms... But it didn't actually measure it. As such, it has no value and no meaning, doesn't relate properly and confuses the hell out of just that one dimension.
(An analogy would be taking all of the personality disorders associated with high IQ and testing for them and calling it the "high iq group". Is it surprising when they don't do better in RL, despite IQ being related to performance/achievement? Is it surprising when there is an unusual population distribution? Yah.)
Oops, I let a bit too much come out this time, perhaps... [/MBTI rant over]
To summarize don't use IQ to type, it doesn't help (except to identify low IQ people, I suppose

)
This is where, contra what I posted above, Keirsey's theory of tactical intelligence seems veritable. Take a reasonably smart pencil-neck and drop him into a room of civil engineers, or mechanics, or foremen talking their profession: he will come off like a fool.
Is the opposite true? Yes. That means it has to do with the transfer - ie: the skills, the experience and the environment.
I'll even go as far as saying that dropping a physics doctorate into my job wouldn't be at all scary, but I'm pretty sure trying to teach any of his material would be way beyond me. And would be, 3-4 years later... probably forever. The doctor would be able to my job by the end of the week. (My job falls in the 90-120 range, physics doctorates in the 125-150 range, roughly.)
And of course, FWIW, if you are talking about the mechanical engineer/civil engineers... their group IQ is around 120-130.
I also remember a study with car mechanics a long time back that had no formal training, in which they were average or above in IQ. I also remember technical schools doing it, in which mechanics (avionics, etc) were notably higher, roughly on part with arts student IQs.
It might be worth picking groups that aren't already above average when using examples.