The house band, known collectively as The Wrecking Crew, was under the musical direction of Jack Nitzsche and included:
Drummer: Hal Blaine
Electric bass player: Jimmy Bond
Guitarists: Tommy Tedesco, Bill Aken, and Glen Campbell
Upright bassist: Lyle Ritz
Pianist: Leon Russell
Saxophonist: Plas Johnson
...and others.
I have always loved Leon Russell’s electric piano work on Gary Lewis and the Playboys “Everybody Loves a Clown.”
https://www.youtube.com/watch?v=Jk-BAwHkwL0
And don’t forget Carol Kaye who played who played the bass intro to Glen Campbell’s “Wichita Lineman.”