Here's an earlier reference to the Rex:

The Bakersfield Californian from Bakersfield, California · Page 15
https://www.newspapers.com/newspage/3523425/
287 IFOR RENT—3-room furnished flat with sleeping porch; close in; J23. ... See Mr. Turner at Savoy hotel at Taft, California, after Monday. ... Box 62, Californian: 287 WANTED—Olrl for soft drink and light lunch, counter, at Rex Pool Hail.

The newspapers site tries to get you to buy the paper, or pay to see the actual ad. "Oirl" would be what we in New Yawk knew as a "Goil." Incidentally, the Savoy Hotel also was known to play a hand or two of cards from time to time.

As the Rex was described as a pool hall, I don't know if the Rex Smoke Shop was the same place. Maybe. Thanks for your ongoing research!