At B1 in the English Vocabulary Profile, ‘either’ is listed as:
PRONOUN; DETERMINER: One of two people or things when it is not important which
At B2 ‘neither’ is listed as:
PRONOUN; DETERMINER not either of two people or things
C1 English Grammar Profile point 60 in the category of DETERMINERS & quantity is defined as:
‘either’ and ‘neither’ with singular nouns.
An iWeb search for either|neither _nn1
1 EITHER WAY 180299
‘either way’ is listed at B1 in the English Vocabulary Profile:
to talk about two possibilities where the result will be the same
For example:
Either way, they’ll call him a coward and I don’t see how he can live with that.
2 EITHER SIDE 102291
either side/end, etc. is listed at B2 meaning each of two sides, ends, etc.
3 EITHER CASE 26335
4 EITHER PARTY 17779
5 EITHER END 15051
6 EITHER DIRECTION 12260
7 NEITHER SIDE 6167
8 NEITHER PARTY 5466
Is it an affair if neither party is married?
9 EITHER TYPE 4308
10 NEITHER TEAM 3760
11 EITHER TEAM 3295
12 EITHER PARENT 3051
13 EITHER HAND 2947
14 EITHER OPTION 2800
15 EITHER METHOD 2551
16 EITHER PLAYER 2248
17 EITHER SEX 2027
18 NEITHER MAN 2002
19 EITHER SPOUSE 1642
20 EITHER GROUP 1603
21 EITHER GENDER 1566