Only recently has India developed nuclear weapons which could hit China's main cities (Beijing, etc.). They did not have this in the 1980s. Countries only use nuclear weapons when they feel as if they have no other choice, and this is why Indo-Pak nuclear TLs work because India could very well march onto Islamabad and force Pakistan to launch their nukes, but neither India nor China could march on to each other's capitals. I suppose the most plausible scenario is that a particularly mentally instable man takes control of either India or China, goes to war with the other, and when things don't work out he just nukes the soldiers of the other country in the Himalayas.
The Sino-Pakistani alliance is extremely well established, though; Pakistan is China's main bridge to the Islamic world, having played a key role in bridging the communication gap between the PRC and the West by facilitating U.S. President Richard Nixon's historic 1972 visit to China, with the relationship between Pakistan and China described by Pakistan's ambassador to China as "higher than the mountains, deeper than the oceans, stronger than steel, dearer than eyesight, sweeter than honey, and so on." Pakistan is China's biggest arms buyer, counting for nearly 47% of Chinese arms exports, with the Pakistan-China relationship considered in global diplomacy to be the closest equivalent to the Israel–United States relationship. When confronted by US officials about Beijing's uncompromising support for Pakistan, Chinese General Xiong Guangkai famously said, "Pakistan is China's Israel." Pakistanis hold the singular most positive opinions of China and Chinese influence in the world, and Chinese people hold the 3rd most positive opinions of Pakistan's influence in the world, behind only Indonesia and Pakistan itself.
So then, bearing all that context in mind, couldn't a limited Sino-Indian nuclear exchange easily be facilitated by all of those factors you cited- with an Indo-Pakistani conflict in the 80's resulting in the Indians marching on Islamabad, driving the Pakistani to launch their nukes out of desperation, which in turn angers the Indians into launching their own nukes at a few Pakistani cities in retaliation, as well as increasing the calls for the outright dissolution and re-annexation of Pakistan. Which would then be enough to force the hands of the Chinese, necessitating their firm intervention on the Pakistanis' behalf, by launching a few nukes of their own (with the Indians, at this stage, still not possessing nuclear weapon delivery systems capable of hitting China's main cities back- though if the Chinese had nuked Indian cities, the Indian leadership would certainly have attempted to retaliate, and probably managed to nuke a few targets in the
Chengdu Military Region, but been hard-pressed to strike any deeper into China than that), forcing the Indians to back down and accept a negotiated armistice with Pakistan, as opposed to the Indians' ultimate ambition of Indian re-unification via the elimination of Pakistan. Sounds feasible?