Thomas Brothers Maps invested a lot when developing their GIS system to create their digital mapping system. Though the first "digitally produced" map was Sacramento County-1990, the development began back in 1986. I expect that their map projection equations are a well guarded trade-secret, which Rand McNally now owns. I'd don't know those equations, but would also like to know them.
There are 9 projections covering the 48 states. If you know the equations for Los Angeles, it is valid across California & Nevada. Oregon & Washington have their own projection. Arizona, New Mexico, Colorado, and Utah share another projection.
I do know this...
As many know, the page grid is an exact 1/2 mile square, or 2640 feet by 2640 feet. The coordinate measurement unit is 1 foot.
To determine the Thomas Brothers XY Coordinate, get one or more of the Thomas Guide CD- ROM maps, which were recently discontinued. The last ones produced for certain California counties were the 2008 edition. Last editions for Seattle, Portland, Las Vegas, and Phoenix/Tucson were the 2007 edition. Each is still available on the Rand McNally website for $20.
When you geo-code a group of addresses, you'll see an output file with the TGXY coordinates and Lat/Lon for the addresses you specified, and the page # and grid that point is in. Once that file is open, you can click on the map to add additional geo-coded points, which will also provide both the coordinates. The output file is saved in an Access database ".mdb" file.
If you know a lot about map projections or solid geometry, the set of corresponding TGXY and Lat/Lon coordiantes will provide you some good data for testing.
As you mentioned San Diego Page 1297, I'll provide its bordering coordinates.
West x=3062760
East x=3086520
North y=0985040
South-y=0966560
This is not in range of the "TBXY" you found on Google. Maybe it's the same projection, with a relocated origin.