The best development I've seen on this is Rabbi Yehuda Herzl Henkin's Contemporary Tseni'ut. It appeared in Tradition 37:3 (2003), as well as its own book. The Tradition article is available online, paid subscription required. Here's his conclusion, as relates to your question:
It emerges from Rashi, Yerushalmi and Korban ha-Eda that peritsut
in exposure of the upper arms comes not from the arms themselves, but
from the body being visible via the arms; this, then, is what Sefer
Rokeah means by zero’oteha megulot, the same language as zero’oteha
halutsot in the Yerushalmi. This is a powerful source for limmud zekhut
in behalf of otherwise modest women whose sleeves do not reach to
their elbows.
A typology can be established, then, as follows:
1. sleeveless dresses—forbidden by all opinions, as body can
be seen.
2. short sleeves, loose—forbidden by all opinions if body can
be seen.
3. short sleeves, tight—body cannot be seen, but forbidden if
most of the upper arm is uncovered (rubo ke-kulo)
4. sleeves half-way to elbow—forbidden because of tefah
meguleh, room for limmud zekhut
5. sleeves to within a tefah of the elbow—minimum permitted
6. sleeves to elbow—recommended
7. sleeves to below elbow—first level humra
8. sleeves to wrists—second level humra.
This does not supplant any communal or familial minhag.