I had never encountered farnisim before I had read this question, but older people where I grew up used to say things like, “ando enfarnesiado,” meaning ‘worried and upset’. Now that was not in Brazil; it was Portugal some 50 km north of Lisbon. It turns out that farnizim or farnesim is a centuries-old variant of frenesi, and it has survived to the present day both in Brazil and Portugal.
The earliest form recorded in Portuguese is however farnesia, in the 13th-century Crónica da Ordem dos Frades Menores (1209-1285); the sense was the original one of ‘delirious state’ (Corpus do Português):
E alguuns, pensando que estava com farnesia de fevre ou d'evaeçemento, tornaromno ao leito.
Frenesi is recorded in the 15th century (Houaiss, Lisboa 2003), and Raphael Bluteau records farnesis e farnetico in his 1713 Vocabulário Portuguez e Latino and at last farnesim in the 1727 Suplemento:
Eventually frenesi prevailed in standard language, being etymologically correctly derived from Latin phrenesis. But farnesim survived in many regions. Dictionaries simply say it is a variant of frenesi, but as the word exists as multiple regionalisms, its use varies. From what I found it can mean ‘irritation, impatience, nervousness, agitation’ and perhaps, in Portugal, ‘hurried activity’.
Aulete places it in the Brazilian Northeast, but Houaiss (Lisboa, 2003) simply says it is a Brazilian word. Most examples in the web come indeed from the Northeast, and it appears in the online Enciclopédia do Nordeste, mentioned in Guilherme’s answer, which mentions Piauí, Paraíba and Ceará. And we find it in this online Dicionário Pernambuquês.
But we find examples in Acre (2005), in this 2014 Quatro Soldados by the Gaucho Samir Machado de Machado (although this one may be a deliberate archaism) and in stories by the Mineiro João Guimarães Rosa (1908-67).
In Portugal we find it in this 1950 Vocabulário Madeirense and in this blog (somewhere in central Portugal, 2011): “começou o farnesim da apanha da fruta.” From the context it appears to mean ‘excitement and rush’. I know all about the rush to harvest grapes when they become ripe. And here someone complains about being “enfarneziada”, and here are few examples of people being accused of “enferneziar” others.