I have not been caving in Sequoia National Park but here is a link to some caves in the park and descriptions for them:
http://www.nps.gov/seki/naturescience/c ... UMP_114864Since you were not able to reach a representative of Sequoia National Park, I would suggest that you contact one of the caving organizations in California for more information about caving in Sequoia National Park. I believe that Soldier's Cave in Sequoia National Park is a popular wild cave that cavers go to. The closest caving organizations (known as grottos) to Sequoia National Park are the San Joaquin Valley Grotto (based in Fresno, CA) and the Los Angeles area grottos: Southern California Grotto and the Desert Dog Troglodytes.