It's more obvious when we're talking about a positive sentence like:
l'un et l'autre viendront => both are coming => plural.l'un ou l'autre viendra => only one is coming => singular.
But when it is negative:
ni l'un ni l'autre = pas l'un et pas l'autre => so it can be plural no?
Multiple sources suggest both singular and plural verb forms are possible for ni l'un ni l'autre:
http://bdl.oqlf.gouv.qc.ca/bdl/gabarit_bdl.asp?id=1490#:~:text=Lorsque%20le%20sujet%20est%20ni,deux%20noms%20coordonn%C3%A9s%2C%20est%20pluriel.
https://www.gymglish.com/fr/frantastique-orthographe/regles-orthographe/ni-lun-ni-lautre-nanont-raison
https://www.btb.termiumplus.gc.ca/tpv2guides/guides/clefsfp/index-fra.html?lang=fra&lettr=indx_catlog_n&page=9WmCJCDuX_J0.html