Why Pakistan has emerged as a mediator between US and Iran (apnews.com)
'Both because it has relatively good ties with both Washington and Tehran and because it has a lot at stake in seeing the war resolved.' Previous US-Iran talks had been done by Oman, Qatar, and other Middle East nations, but they're involved in this war (bombing on their territory).
Neighbor to Iran, longstanding good ties with US (Pakistan joined Trump's Board of Peace, also, despite disapproval from Pakistani Islamists). Good working relationships with both and others involved, including KSA. Pakistan doesn't get along with Israel because of the Palestinian issue. Pakistan also helped in US-China talks in 1972 and in 1988 helped in what led to the Geneva Accords. Pakistan mediates between the Afghan Taliban and the US.
5m Pakistanis working in the Arab states, sending home as much money as Pakistan's exports. Pakistan's fuel prices are up 20% so far.