Anonymous“ Do the modals 'should' and 'might' have any sense of the past? I think they are all present in their implications.”
Yes, they do have a sense of the past. Modals in subordinate clauses often take on the characteristics of the time frame set up by the main clause.
The teachers gave these orders:
If anyone finds the answer, he should (at the time of finding) notify the teachers so that they may verify it.
Backshifted:
The teachers had given these orders:
If anyone found the answer, he should (at the time of finding) notify the teachers so that they might verify it.
Thus:
had given is the backshift of gave; found, of finds; should, of should; might, of may. (should is its own backshift.)
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Your second example works the same way. The only difference I notice is the addition of a different kind of should in the if clause -- "evaluative should", not the "advisability should" seen in other places in your two examples.
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Uses of should are sometimes somewhat indeterminate in tense, and other tenses in the sentence have to be used as clues.
CJ