There are obscure British accents where words spelled with eigh like eight can have a different vowel from words spelled with "long a" like late or words spelled with ay/ai/ey/ei. This is not technically a split, but the lack of a merger that is present in nearly all other accents of English.
Historically, eight had a fricative consonant [ç] before the [t], which caused the preceding vowel to diphthongize, while the vowel in late comes from the Middle English monophthong [aː], which ended up being raised and fronted to [eː] and then diphthongized to its typical value of something like [eɪ~ɛɪ~ej~ɛj] in most accents.
Wikipedia says that in some accents, the vowel of words like eight and weight developed differently due to the presence of the fricative:
/h/ spelled -gh- is realized as [x] even today in some traditional dialects of northern England and more famously Scots. Some accents of northern England lack the /x/, instead exhibiting special vowel developments in some such words; for example, night as /niːt/ (neat) and in the dialectal words owt and nowt (from aught and naught, pronounced like out and nout, meaning 'anything' and 'nothing'). Also, in northern England, a distinction is often preserved between the vowel /ɛɪ/ in words like weigh, weight and eight, and the /eː/ of wait and late (the northern realization of the vowel resulting from the pane-pain merger).
There is also a third set of words that can have a distinct vowel sound: certain words, usually spelled with ay/ai/ey/ei, that had some diphthong like [ai] or [æi] in Middle English. In most accents, this merged with the late vowel, but in some British accents, it remained distinct. Wikipedia says
The pane–pain merger is a merger of the long mid monophthong /eː/ and the diphthong /ei/ that occurs in most dialects of English. In the vast majority of Modern English accents the vowels have been merged; whether the outcome is monophthongal or diphthongal depends on the accent. But in a few regional accents, including some in East Anglia, South Wales, and even Newfoundland, the merger has not gone through (at least not completely), so that pairs like pane/pain are distinct.
A distinction, with the pane words pronounced with [eː] and the pain words pronounced with [æɪ], survived in Norfolk English into the 20th century. Trudgill describes the disappearance of this distinction in Norfolk, saying that "This disappearance was being effected by the gradual and variable transfer of lexical items from the set of /eː/ to the set of /æɪ/ as part of dedialectalisation process, the end-point of which will soon be (a few speakers even today maintain a vestigial and variable distinction) the complete merger of the two lexical sets under /æɪ/ — the completion of a slow process of lexical diffusion."
Walters (2001)[8] reports the survival of the distinction in the Welsh English spoken in the Rhondda Valley, with [eː] in the pane words and [ɛi] in the pain words.
In accents that preserve the distinction, the phoneme /ei/ is usually represented by the spellings ai, ay, ei and ey as in day, play, rain, pain, maid, rein, they etc. and the phoneme /eː/ is usually represented by aCe as in pane, plane, lane, late etc. and sometimes by eCe and e as in re, cafe, Santa Fe etc.
When words like pain and pane are distinguished by non-native speakers, it is most likely an example of spelling pronunciation. I know of no American English accent that has this distinction. Different accents of American English may have more or less use of a more monophthongal value [e] vs. a more diphthongal value like [ei̯], but these are allophones, not distinct phonemes. (I left out length markers because in English, phonetic vowel length is highly dependent on context: a vowel before a tautosyllabic phonologically voiceless consonant as in wait or late will be relatively shorter than a word-final vowel as in way or a vowel before a phonologically voiced coda as in wage, paid).
As other people have mentioned, the word ate is a special case: in a number of British English accents, the spelling has an irregular correspondence to the pronunciation, and the vowel may be short: /ɛt/.
/ɛt/contrasting eight/eɪt/, but none of the other words you mention have this vowel in these dialects, they are all/eɪ/.