I've never thought of this before but probably it corresponds to octopus.
This is because it's common across languages that animal names are used to insult someone.
In English, we say chicken to call coward people, and donkey to call idiotic people.
It's a very interesting question, because the both meanings seem appropriate.
So I'd be grateful also to listen other opinions of the native speakers.
Do all of you associate this type of タコ usage more with octopus than with callus?
In my area in Japan, many people sometimes use タコ for insulting someone:
I don't know its etymology, but I first heard the expression in around 1980 spoken by a 19-year-old guy.
I thought that it means probably 蛸（octopus) or maybe 凧(sky kite) but never thought it as 胼胝 (callus).
I thought it came from タコ踊り（＝ダサい踊り）.
タコ踊り is a funny and weird dance with a mask of an old man whose mouth is imitating an octopus's mouth. The movement of the dance itself is somewhat imitating the motion of an octopus. It's basically a traditional Japanese dance.
However, if a guy danced very poorly in a discotheque, his dance was described as タコ踊り in around 1980.