Short answer before the long one: There isn't much in the texts and when they were mentioned, it would be from a Chinese perspective but archeological research has helped and two works that give a history of the "Nanman" would be Bin Yang’s “Between Wind and Clouds: The Making of Yunnan” and John Herman’s “The Kingdoms of Nanzhong China's Southwest Border Region Prior to the Eighth Century”

In terms of elephants, that is an invention of the romance as you suspected. While they produced excellent horses and were able to provide elephants as tributes, there isn't evidence they used elephants in battle.

Longer Answer (though I would recommend those two free books, keeping focus on my answer culture and elephants rather then the history of the groups): Knowledge is limited with lack of records, I have not seen anything that goes into detail about their culture, what it looked like bar this paragraph from Yang's chapter 2:

"Due to its geographic location, however, Yunnan has had closer ethnic and cultural associations with Southeast Asia. Ling Chunsheng has listed fifty common cultural features among Southeast Asian peoples, such as a patronymic system (fuzi lianming zhi), secondary burial/bone-cleaning burial (xiguzang), cliff burial (yazang), pile building (ganlan), and tattoos (wenshen). These customs have been found from the Pacific to Madagascar. For example, bronze drums have been found in Vietnam, Malaysia, Thailand, and Yunnan, although arguments about the origin and routes of diffusion continue. All of these probably resulted from prehistorical migrations of which scholars know very little. Considering these facts, more and more scholars tend to put ancient Yunnan into the category of Southeast Asia rather than East Asia. So, what was the role of Yunnan in the origin and development of Southeast Asian civilization?"

The Nanzhong area had many communities (Yelang, Qielan, Louwo, Tongbing, Gouting, Jinsang and Bi) that got put under one umbrella by terms like Nanman. Their lands had rich plains where they bred well regarded horses (something that would be useful for Shu and, via trade, Wu who controlled none of the traditional breeding grounds during the three kingdoms), mountains and rivers that helped for defenses and lots of mineral wealth like bronze, silver, copper. They traded with the Chinese provinces of Ba, Shu and Jiao while trading elsewhere like the modern Myanmar, Tibet, Vietnam.

Distance and terrain meant it was difficult for Qin, the short lived Xin dynasty and Han to take over, if the tribes bandied together they could make things very difficult. The Han tried to maintain control with limited success by relying on the local powers and if revolts happened then dividing the communities to help their armies put down revolt, but over time, the old communities seem to have faded away and the powers came to be the local magnate families, descendants of Han officials who had settled there, married into the local populace and adopting some customs but very much Han figures. The major powers were, by the three kingdoms, the local Chinese magnate families: Yong, Meng, Li, Cuan, Jiao, Lou, Liang, and Mao while the region had suffered major economic damage when the revolt of 176 was put down with considerable force

The "Nanman revolt" of 219 to 225 was actually a revolt of some powerful Chinese families (though not all, the Li family under Li Hui would fight for Shu and it is not clear which side Cuan family was actually on) under the command of one such magnate Yong Kai. Some tribes like Yuexi's Sou chieftain Gao Dingyuan did take part and magnate Meng Huo was able to use his connections to help bring some of the indigenous communities into the revolt. In 225 Zhuge Liang, now with Shu not at war with Wu, led a force of three armies (others under local Ma Zhong and Li Hui) to put down the revolt which was done fairly quickly and then Zhuge Liang made administrative rearrangements to try to win over the local families and get access to the resources. This was mostly successful though Shu figures did have some battles left to fight in the decades to come and expanded their control. Elephants are not mentioned at all in any of these wars as op suspected.

The novel romance of the three kingdoms focuses on that last year. It changes from magnate to the entire thing being led by Nanman, Meng Huo goes from Chinese family to a Nanman King with a Nanman wife and family. Instead of Chinese vs Chinese it is Zhuge Liang, the epitome of civilization and scholarship vs the barbarian natives. It is four chapters (Wu and Wei's taking of their starting lands struggle to get half a chapter each) of something that provides something completely different from the rest of the 120 chapters.

The Nanman are meant to be strange and exotic, they have horrible uncivilized practices (examples of things listed and strangeness in spoilers)>!human sacrifices, rejecting medicine for shaman's, allowing adults to marry who they will without requiring parents permission and Zhuge Liang stops some of the practices, teaches them proper governance. Meng Huo is not put in the best of light with even his own family insulting him, the queen Zhu Rong personally fights. They have magical poisonous springs, Rattan armor!<.

On elephants, it is part of that strangeness that only Zhuge Liang has the perseverance and the wit to counter but the elephants themselves aren't presented as a regular Nanman tactic or thing it is used for two specialist cases.>!King Mulu whose specialty is magic and control of wild animals which combined he uses to initially defeat Shu forces but Zhuge Liang had already prepared and next battle counters the magic, Mulu rides an elephant. The giant King Wutugu who eats only snakes, lives in caves and has the Ratten army also rides an elephant. !<

Hope that helps

Sources: As well as the two books listed at top, Chang Qu's gazette Huayang Guo Zhi which is the main source on Shu's dealings with the people of Nanzhong