There's no weather station on Mt. Whitney but there are a few automated weather stations that are sort of nearby.
Try this link if you haven't already;
https://mesowest.utah.edu/. Here's another link if you haven't gone this route either;
https://www.wrh.noaa.gov/map/?obs=true&wfo=vef. The nearest automated weather site to Mt. Whitney is the Crabtree Meadows Station. However, I don't see any barometric pressure data. Perhaps clicking on the FAQ/Data Issue link might provide some insight on barometric pressure data you're looking for.
At one time White Mtn. to the NE of Mt. Whitney had an automated weather station that was the part of the Western Regional Climate Center (
https://wrcc.dri.edu/) but it's been off-line for a few years now. I think it was very hard to keep running because of the very high winds it often experienced. Its remoteness doesn't help either plus it's nearly impossible to access in the winter. Here's the site but there's no current weather data;
https://wrcc.dri.edu/weather/wmtn.html. Historical data seems to be available but I haven't figured out how to access it.
Good luck with what you're looking for.
