Welcome to the forum. Always glad to see somebody willing to dig for information.
The only place you might find Frio County production history that might be as far back as the 1930’s is the Texas Railroad Commission’s archieves in Austin. RRC’s online records only go back to the 1990’s. In any case I don’t think you could pin down drilling that ever took place in a particular part of the county without more information, like the survey/abstract number, or Block and Section, of those two 160 acre tracts you mentioned.
The deed records in the County Clerk’s office for Frio County is a logical place to look for more information, but a quick check didn’t turn up anything there in the name of your grandfather or W.K. Quigley. Here’s a link where you can try you luck at free online searching in those records. Use the first pull down menu to select Frio County https://public.lgsonlinesolutions.com/ors.html
You didn’t say if your grandfather had lived in Frio County, or where you thought his dealings with Mr. Quigley might have taken place. The Bexar County deed records show a guy named W.K. Quigley was doing business in San Antonio in the 1920 and 30’s, possibly in real estate.There’s also a Travis Building in San Antonio. It was completed in 1926 and originally was referred to as a “commercial” building but a couple of years ago was converted to apartments. I don’t know if Quigley had an office there or know what the “C. 1916” at the end of that notation might mean but thought this might give you a starting point.
Here’s a link to the current status of the building. https://www.travisbldg.com/