Of course a diligent search is required. You cant even claim that evidence is lacking unless you've taken a good look-see. You need a basis for the claim to be reasonable.
I think you're missing the point here, rather.
Let's take the Martian example: You set up a hypothesis; There is intelligent life on Mars. Null hypothesis: There is no intelligent life on Mars. What would provide evidence for the hypothesis? The presence of buildings or structures generally associated with higher life-forms, or photographic evidence of a Martian creature. Research is conducted in the form of a photographic survey of Mars. No buildings or structures are found, nor photographic evidence of a Martian creature. Hypothesis unproven, null hypothesis upheld.
However, then one could conjecture that an alien intelligence may not build structures that we would associate with higher life-forms, or they may be subterranean. Thus, this hypothesis - "Higher intelligence on Mars exists in subterranean environments" has no evidence for or against. Thus, the null hypothesis - "Higher intelligence on Mars does not exist" - remains unknown as well. In the absence of evidence, one cannot make a statement either way.
Scientific method - learn it, know it, love it.
Absence of evidence by itself demonstrates nothing. It can certainly point towards a conclusion, but it cannot alone be used to justify a positive claim.
Correct. The lack of evidence alone is not sufficient to make a definitive judgement. BUT, it is one piece of evidence to condsider alongside any others.
But the lack of evidence alone isn't evidence. At the point that a diligent search has been conducted according to accepted scientific principles, a hypothesis should be either proven, or the null hypothesis upheld.
Seeing nothing relevant after a search = absence of evidence.
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No, seeing nothing relevant after a search = unsupported hypothesis, not absence of evidence.
If we're conducting our research properly, that is.