Where is it located?
Most liquid powered engines are/were powered by a fuel (RP1 or kerosene and liquid hydrogen) plus an oxidizers (usually liquid oxygen and rarely flox or floridated liquid oxygen the that was very unpredictable). The test facilities were usually upright towers and tank, but there were some below ground systems for unique tests of developing or proving engines. the liquid oxygen powered engine contained a great deal of power per pound, but the facilities had to be built to avoid the use of any asphalt pavement (a fuel). The liquid hydrogen was also very powerful and dangerous, requiring frequent purging of the tanks and traveling in pairs if there was a non-purged tank because it is easily ignited and burns at high temperatures with a colorless flame in the daytime. All of the liquid oxygen and hydrogen had to be in cryogenic piping The most common engine was the engines that powered the Saturn rockets. If it was a test site for liquid engines the shaft could lead to many different possibilities.
Solid propellant engines were tested with the flame pointing up and could not be controlled once started and usually did not have the ability to be started and stopped. they are still used and ejected once the fuel was used.
Some of the common test areas for liquid powered engines were the Santa Susana/Simi Valley of CA, Edwards AFB an area near Reno, NV Missouri and Huntsville AL. There were some test facilities for solid fuel engines near Sacramento, CA. You never knew what to expect because of the experiments and rapid changes.
If you find out about the type of engines tested and provide site location this may narrow the possibilities, but frequently land owners may be reluctant to offer information because of the potential pollution problems that never seem to go away. Some sites were on government property because of security concerns.
I worked in the industry as a facilities engineer for several years and it was the most education I ever got ranging from building design, wells, dams/holding ponds, roads and modifying test stands (including dynamic testing with all joints instrumented) when we could get access around the engines.
Dick