[Note: I have solved only five of the ten clues and the meta puzzle. Clues I didn't solve reference the actual solver. If you like this answer, please consider upvoting these answers, too.]
Strange non-uncle, perhaps? (4)
RARE — def. strange; UNCLEARER (perhaps?) − UNCLE (non-uncle) = (RARE*). Mike Q has found the answer, RARE.
One ton one under sun begun, perhaps (10)
MONOTONOUS — &lit. and def. by example, because of the repeating un-un-un's; MONO (one) + TON + UOS (first letters of One Under Sun). Solved by Neil W.
Weird Y (8)✻
ATYPICAL — def. weird; indirect anagram (weird) of CAPITAL Y. Solved by Mike Q.
Mixing endless accessories (5)
BLING — def. accessories; BLENDING (mixing) − END (end-less). Solved by Neil W.
Disconcerting major exit! (6)
ESCAPE — &lit.; anagram (disconcerting) of SPACE (the extra space between the first two words) + first letter (major) of Exit; Found by F1Krazy.
Perhaps, a resting spot with an eccentric, eccentric start (9)
PERCHANCE — def. perhaps; PERCH (a resting spot) + AN + CE (starting letters of eccentric, rearranged or eccentric). Thanks to Silenius for correcting the wordplay.
Direct, and headless (7)
COMMAND — def. direct as verb; COMMA (the punctuation mark in the clue) + [a]ND headless. Found by Techidiot.
Perhaps, every permuted tie and portion (12)
ALLITERATION — &lit. and def. by example of words beginning with P and probably read as "Perhaps punctuation ..."; ALL + (TIE)* + RATION
UNDERLINE — def. emphasise; UNDER + LINE, represented by the hyphen
Gained for the first mixture with. (8)
PROFITED — def. gained; anagram of FT (first letters of for and the) and PERIOD, the punctuation at the end.
If we take the solved clues and take the letter at the position that corresponds to the number of words in a clue, we get:
RAR E — Strange non-uncle, perhaps? (4 words)
MONOTO N OUS — One ton one under sun begun, perhaps (7)
A T YPICAL — Weird Y (2)✻
BL I NG — Mixing endless accessories (3)
ES C APE — Disconcerting major exit! (3)
PERCHANC E — Perhaps, a resting spot with an eccentric, eccentric start (9)
CO M MAND — Direct, and headless (3)
ALLIT E RATION — Perhaps, every permuted tie and portion (6)
U N DERLINE — Under-emphasise (2)
PROFI T ED — Gained for the first mixture with. (6)
And the meta answer is: ENTICEMENT
✻ The clue "Weird Y" was changed to "Weird, weird Y" in order not to make "weird" do double duty as definition and anagram indicator. The OP said that changing the clue would break the meta, so the meta had something to do with the clue itself, probably with the number of words. This information helped me to find the meta before the last three clues were solved and privided at least one letter for the answers to these clues.