I can pretty much answer your questions as I hung out around LAUS (formerly LAUPT) as a kid and later, starting 18 years ago as an Amtrak employee. The tracks that the Private Passenger Cars and Equipment are parked on today were orriginally placed there when the station facility was built in 1939 to serve as loading and unloading for U.S. Mail on Passenger Baggage and Mail Express Cars. They were numbered from West to East as track 41 through 45. They were referred to as the "Mail Tracks." When Amtrak started on May 1st, 1971 a lease agreement was entered between them and the LAUPT Corp. (the Terminal R.R. that was owned by SP, UP & ATSF and this C.O. only existed on paper) to lease a certain amount of tracks on an individual use type basis. This lease did NOT include tracks 41 through 45. Shortly after that a meeting was held between SP, UP & ATSF and the LAUPT Corp. to decide what to use the remaining tracks for. All 3 agreed to use these tracks for use by the 3 R.R.'s business cars. To have room to park work equipment vehicles among other things, it was decided to take out track #43. This track was then paved over with asphalt. The other 4 tracks were equipped with stand-by power hook-ups and phone jacks for SP, UP & ATSF telephones. UP was the lst to stop using these tracks in the mid 1970's, having equipped "Freight House 4" and the spur off of it at East Los Angeles Depot with the hook ups mentioned above. Then close to 1980, ATSF stopped using them as they built a business car track with these same hook-ups at their office at the time on Sheila St. in Commerce. Sometime in the mid 1980's these track were referred to as the "Private Car Park". SP continued to use all 4 tracks for their use. At the end of the 1980's when Union Station was sold to the Katellus Corp., the LAUPT Co. ceased to exist but the 3 RR's retained rights to use these tracks on a case by case basis. At this same time all tracks in the Terminal were turned over to Amtrak for their full use and control. It was then up to Amtrak to decide their use. After this, in addition to SP using them to park and store their business cars, Amtrak would occasionally park private cars on them. Amtrak also would use them to store freight engines for SP to pick up after they brought Amtrak trains in. About 1991 an Amtrak Supervisor of Opertaions named Bob Bonham began dubbing these as the "Garden Tracks" because of the hedges and other plants on the outer edge that you would find in someone's garden. He thought the name would be a good fit, but it was more of an effort to have his named assocatied with the tracks in R.R. history. I guess he thought he would be looking forward to telling his Grandchildren someday that the name came from him. A few years after that, a Private Car Rail Co. leased the 4 tracks from Katellus Corp. for long term storage. This Private car co. began letting other private car owners use these tracks to store their cars. I left Amtrak 12 and a half years ago and moved out of the area 10 years ago and have not kept up these tracks, but I do know that they are still being used by Private R.R. car owners in the area to store their cars. Amtrak and the freight R.R.'s no longer use them. Hope this is helpful and answers your questions.
As my co-worker Mike would say, "Amtrak 306, you look good by the tower, your markers are lit and I'm over."