The etymology of these words (pedantic and pedantical) is a little confusing because of the forms in which they entered English from Old French.
PEDANTICAL: The original form from which pedantical (1580s) was derived was French pédantesque, which is pronounced pre-don-tesk. According to Etymology Dictionary, the earlier derived pedantical first appeared in writing in the 1580s in the Renaissance during the Elizabethan and Jacobean ages.
Related [to pedantic c.1600]: Pedantical (1580s); pedantically. (Etymology Dictionary)
It was derived by adding the suffix -al to the Middle English form of the French pédantesque.
Perhaps the predecessor to "pedantic" was John Donne's pedantique, still showing the French origination in the spelling, in his poem "Sunne Rising" (circa 1593) in the phrase:
Sawcy pedantique wretch, goe chide Late schooleboyes
PEDANTIC: Pedantic came later in the 1600s ("pedantic (adj.) formed in English c.1600, from pedant + -ic") and is derived from Middle French pédant or from Italian pedante. The derived form is pedant + suffix -ic. The French and Italian both mean "teacher" and provide a different root source for pedantic (teacher: pédant/pedante) than the root source for pedantical (showy about being learned: pédantesque pedagogue).
PEDANT: (root of pedantic) Today to be a pedant means to be:
a person who relies too much on academic learning or who is concerned chiefly with insignificant detail (Collins Dictionary)
Pedant may also relate to the Latin paedagōgus.
The denotations of pedantic and pedantical are the same: a person has a sense of over importance in learning and pays undue attention to minute detail in academic pursuits or issues.
The connotation is a negative one suggesting arrogance and disdain for others who have lesser academic or professional attainments. Though pedantic/pedantical are at times misused to apply to anyone in any endeavor, the words are correctly limited to application to people in academic or professional fields. Remember that today usage of pedantic/pedantical is identical though their roots are different: both now comprise equivalent adjectives for the noun pedant.