Where can I learn more about Military Sea Lift Command Pacific and find command ball caps or Type III shoulder patches for this unit?

I think you might be narrowing your information a bit to 'Pacific MSC' specifically. The Pacific MSC is a regional arm (Area Command) of the Military Sealift Command overall.

Some quick snippets of information (you can read through the rest at the links below):

• MSC is represented by five geographic Area Commands, which exercise tactical control of all assigned U.S. Transportation Command forces and MSC forces not otherwise assigned to the Numbered Fleet Commanders. The Area Command staffs are also responsible for execution of strategic sealift missions. Area Command Commodores are dual-hatted, each one having a formal relationship with their geographically collocated Numbered Fleet Commander. Under Fleet Command authority, the commander may exercise tactical control of MSC ships assigned to the Fleet Commander, usually as a Task Force Commander.
• Military Sealift Command Pacific (MSCPAC) exercises tactical control over Military Sealift Command (MSC) ships in the U.S. 3rd Fleet area of operations in the Eastern Pacific from the U.S. West Coast to the International Dateline and during a limited number of operations across the International Date Line. During FY 2024, MSCPAC ships delivered fuel, food, supplies and ammunition to U.S. Navy ships, performed a variety of special missions, and transported vital military cargo to and from U.S. and allied nations.
• Thirty-eight Navy Reserve units support MSC operations worldwide, providing critical support to the Combat Logistics Force. Afloat rig teams support weapons and refueling operations, provide integrated sustainment and logistics support to joint forces at expeditionary sea ports of debarkation and embarkation, deliver sustained logistics support to the MSC Fleet, and direct integration of the Strategic Sealift Officers for material and Tactical Advisor support to the Strategic Sealift

I'd start with the MSC 2025 Handbook* as it will likely answer the majority of your questions about the unit, what it does, etc.
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* MSC Ships - https://www.msc.usff.navy.mil/Portals/43/Posters/MSC_USNavyShips-2025.pdf
* MSC Handbook 2025 - https://www.msc.usff.navy.mil/Portals/43/Publications/Handbook/MSCHandbook2025.pdf
* https://picryl.com/search?q=military%20sealift%20command%20pacific
* DVIDS posts referencing Military Sealift Command Pacific - https://www.dvidshub.net/search/2.0?q=Military+Sealift+Command+pacific&unit=Military+Sealift+Command+Pacific
* January 2025 issue of SEALIFT - https://www.msc.usff.navy.mil/Portals/43/Publications/Sealift/2025/01/Sealift-2025-01.pdf

PO3 (Join to see) Below is the Military Sealift Command website. There are phone numbers and an email to contact them for assistance.
https://sealiftcommand.com/contact-us

I Worked For MSC For A Few Years As A Cook .
I Was Based Out Of Norfolk Va , But I Was Assigned To Ship’s Out Of Baltimore MD,Jacksonville FL And Newark NJ.
And Each Ship I Was Assigned To Gave Me A Ball Cap And Shoulder Patches,
You Could Also Buy Them At The Exchange On Base.
I Would Guess You Would Be Home Based In San Diego And Could Go Anywhere MSC PAC Has Ships .
The Crews Onboard MSC Ships Are Smaller Than Navy Ships So You Will Probably Have Your Own Private Room With A Shower .
If The Food Is Anything Like It Was Back In The 90s When I Served On Board, You Will Get Some Fantastic Meals.
We Would Get Some Of Food Stores Through The Supply Chain, But We Would Also Get Cash From The Captain To Buy Food From The Local Grocery Stores .
Surf And Turf On Fridays Was Delmonico Steaks And Whole Lobster With All The Fixings .
If You Have Any More Questions Then Direct Message Me.