Jim,
I believe this is the same Model K Carl Binner (RIP) TX, owned at one point. The smaller wheels with aftermarket demountable rims lead me to that conclusion. Mr. Binner bought the car in about 1955:
If these are the same Model K, the car was originally purchased by a Dr. Raby, and is number 952, one of the last of the approximate 1,000 Model K built and sold. K number 900 sold in February, 1908. 118 Model K were sold in Fiscal Year 1908, with another 42 documented (FMC) sold in 1909 and 4 more in 1910 by Ford (courtesy of Trent Boggess’ database).
The article above, dated July 1970, describes the lineage of the car from the original purchaser, to John Dyson, and about 1955 sold to Karl Binner.
The article below mentions Dr. Raby and wife passing through Clifton TX in their automobile. I have no idea if this was the Raby K, or a car he owned prior or while he owned his “Ford Six.”