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They probably wired it to come on all the time, because they couldn't figure out the problem of why it would not come on properly.
What I'm thinkin as well. If automotive electrical isn't your specialty (which beyond basic stuff definitely isn't mine either, so don't feel bad) then the best course of action would be to find a shop or someone who does it well and pay them to unphuck things. The cooling fan circuit isn't the most complicated thing in the world, and as long as you can find someone competent to diagnose and repair then it probably won't be super expensive either. It gets expensive when somebody who is less than competent starts making guesses and throwing parts at it that don't fix the problem.