You certainly do not want to add a unique index to column 1, as you just said:
Neither columns nor columns2 are unique in themselves.
If the first column comes first, it will be the first in the multi-column index in most databases, and therefore it will be used. The second column is the one that cannot use the index. I would not add one to the second column, if you did not see problems and again, I would add an index not a unique index based on the comments you wrote above.
But SQL lite should have some way to see what it uses, like most other databases, right? Install Pk and see if only column1 uses its queries.
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