(both screenshots from Cambridge English Dictionary website)
And usually, a “short vowel” sound in English followed by a hard consonant is typically written in katakana includes a small tsu. Hat, net, back, bag, and neck are written ハット、ネット、バック、バッグ、ネック.
So I still think it’s a mystery why ネクタイdoesn’t have a sokuon.
I took a quick glance at this paper to see if there was anything that could explain the discrepancy between necktie and necklace, and I didn’t find anything, but it’s possible I just missed the relevant section. At the very least, those words don’t appear in the paper as examples.
That would make some sense. But it’s the opposite: ネックレス and ネクタイ.
@Leebo That’s an interesting study. I certainly didn’t read the whole thing, but beyond phonology, I imagine some of the discrepancies may have to do with what the katakana conventions were when the loanword was imported. This may explain nekutai/nekkuresu.