I never heard about vinegar. Nuts (egoz)ostensibly are equal in gematriah to cheit (sin), so we are noheig not to eat them at this time. BUT, aleph= 1 gimel = 3 vov= 6 zayin =7 and
ches= 8 tes =9 and aleph =1.
You do the math. (I know, I know, one more or less is not significant, so they say. Still, I believe If you are already doing gematriah, do it consistently and don’t kvetch the answer to fit your idea). (and BTW, I do not eat nuts, either, during this time).
In any event, what is the problem with vinegar altogether? The sour taste? If so, cider vinegar and rice vinegar are sweet, as is balsamic. So what is the inyan of this minhag ?