I frankly dint know much about this till i got an A2A to answer this question. In the end, i discovered for myself a very interesting piece of history.
It seems that at the time of the Indian invasion by China, Pakistan was ruled by Ayub Khan, who was in the shadow of Americans. Shah of Iran was also an American puppet and Nehru was depending on America to save his ass if China came calling for it. Under American initiative, Ayub even offered Pakistan's help against the Chinese incursion.
America wanted to recruit India to become part of CENTO or SEATO, to prevent the spread of communism from China. India refused to join, so Pakistan became the regional representative of American strategy to counter the communist threat. America wanted Pakistan to give up all relations with China, and even fight with India.
China was a focus point for America during this time because Americans were aware of the role the communist party was playing in other conflict zones they were engaged in i.e. Vietnam and North Korea.
Nothing came of this request though, because Menon had his doubts about the sincerity of Pakistan's request. It is also interesting to note that there was some tension between China and Pakistan over the shared boundary North of Kashmir.
Looking back, military leaders in Pakistan look at this missed opportunity as the single biggest mistake in their campaign for Kashmir.
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During the 1962 Sino-Indian war, Pakistan did not intervene. India was vulnerable at that time and I doubt if India could have successfully dealt with a two front war - vis a vis with China and Pakistan simultaneously.
Pakistan at that time was ruled by Ayub Khan and if reports are to be believed, he was very tempted to seize this opportunity. Pakistan launching an attack at that moment would have very likely stretched the Indian military to the extreme level, or who knows, even to the breaking point. Regardless, it did not happen and Pakistan remained silent on the military front.
Why???
Because of this man.
Pakistan was a member nation of SEATO and CENTO , and US considered Pakistan as its ally in the region. JF Kennedy made it very clear to Pakistan that they are not supposed to initiate a war against India.
“The Ambassador urged him to send assurances to Nehru that Pakistan would not take advantage of India’s war with China,” Riedel wrote.
In response to that, Khan suggested that “the Americans and Pakistanis work together to seek the surrender of Indian territory just as the Chinese were grabbing land”. However, the US considered this as ‘blackmail’.
Nehru had already sought US’s help in the ongoing war with China. US’s stern warning to Pakistan was relayed by UK too.
“Kennedy’s message to Ayub Khan, reinforced by a similar message from [then British] prime minister [Harold] Macmillan, left little in doubt that the US and the UK would view a Pakistani move against India as a hostile and aggressive action inconsistent with the SEATO and CENTO Treaties,”
Shah of Iran, who was a puppet of US, asked Pakistan to aid India.
As the 1962 war began, the Shah of Iran sent Nehru a copy of letter he had written to Ayub Khan, suggesting that he send his soldiers to fight alongside Indian forces against the 'red menace'
Why US stopped Pakistan?
Mostly because they were aware of the role played by the Chinese in the wars fought by US in Vietnam and North Korea and needless to say, considered China a menace.
“The Americans told Pakistan that the Chinese attack was the most dangerous move made by Mao since 1950 and that they intended to respond decisively,”
However, the war did not last long as China declared unilateral ceasefire.
Pakistan did attack India three years later in 1965 and India replied back appropriately but had Pakistan attacked in 1962 ………..well, not a very pleasant thought!