Imho the most comprehensive treatment of Latin accent (beautifully defined as "anima vocis" by some Roman grammarians) is Leumann, Hofmann, and Szantyr 1977, Lateinische Grammatik. Band I. Lateinische Laut- und Formenlehre. (para 235-246, Betonung und Akzent). Caveat: It is in German.
There is some evidence that even Roman grammarians admitted struggling with Latin accentology, e.g. Probus wrote this (taken from Belov 2005):
Since there is a significant number of exceptions (all of them are rara), I will focus on oxytones for now. The following is my summary of relevant parts in Leumann, Hofmann, and Szantyr 1977, Tronskii 1960, and Weiss 2009/2011.
Oxytone (final syllable accented) as a result of an apocope (of the final vowel) or a syncope of the Inlaut syllable:
a) in some proper nouns or adjectives (containing suffix *ati or *iti): Arpinas (from Arpinatis), Suffenas, Maecenas, (Valerius) Antias, Samnis (from Samnitis); nostras (from nostratis);
b) in some pronominal adverbs: illic, istic; illuc, adhuc; illinc; illac, posthac etc.;
c) in some cases with the interrogative enclitic particle ne: viden (from vides-ne), tanton (from tantone);
d) the short forms of the Perfect: audit (from audivit), intritat (from intritavit), disturbat (from disturbavit), sepeli (from sepelivi), petit, cupit, fumat;
NB: Tronskii 1960 argues such forms were rare.
e) 2SG imperative of duc and dic compounds: educ (from educe), addic (from addice)
NB: Weiss 2009 writes that such forms derived from dico are not attested in Classical Latin (p. 422, footnote 22).
f) Also, ancient grammarians insisted on oxytone stress in some conjunctions: pone (after), sine, ergo, verum (but), in some cases arguably to distinguish those from other homophones. Mancini 1997, however, seems to dispute this.
g) in some adverbs: falso, una, alias;
h) in some interjections: attat, papae (Tronskii 1960, p. 62).
If you read in Russian, I strongly recommend Belov 2005, especially Part III, where he analyzes data from ancient grammarians.