The clue to solving Timbuktu lies in the introtext phrase "each year it erases" Also, there are 16 words, and 4 pairs of sentences, suggesting a 2:1 word:sentence ratio.
each answer word uniquely matches to a sentence. that is, there is only one sentence that contains the set of letters found in each. Thus, the first sentence, (jan 1433) contains the letters needed to form briggs and demarcated.
feb. 1433 contains caracolling and assessment.
so, if you remove from each sentence the letters contained in the matching words, you are left with a subset of letters.
(from the first sentence pair, these are utaputuktuao, and tuuvatoukuet.) looking at these letter groups,it is obvious that they contain almost identical letters, as well as having the same # of letters. so repeat the erasure step with each matched pair. this leaves you with 2 letters remaining from each pair: pa/ve wa/ys wi/th go/ld
and that's the answer.
(the dates/ months are utterly irrelevant,) word:sentence matchings are below.
jan 1433: briggs, demarcated feb 1433: assessment, caracolling apr 1350: twenties, derailed may 1350: syrup, decontamination jul 1342: lambswool, shanghai aug 1342: forefront, voluble oct 1330: jubilee, absurdism nov 1330: titsandass, setoholdings