This aircraft is definitely a SNJ-2. Only 61 SNJ-2s were built. The insignia and tail markings are typical for 1942. The dark painted color is typical of the SNJ-2 in Navy service.
These aircraft were built by North American Aviation at the Inglewood California plant prior to 1941, and later as SNJ-3/AT-6s at the NAA Dallas Texas plant beginning in March 1941. An almost exact view at the same angle of one of the Geico SNJ-2 planes trailing smoke may be seen here. The photograph is not reproduced to protect copyright. North American Aviation, by the way, was responsible for the design, lofting, and prototype assembly of the P-51, all in approximately 90 days. War-time production of the P-51 was at the Dallas plant.
The SNJ-2 is the predecessor of the SNJ-3/AT-6A and succeeding variants that were used as pilot-training aircraft throughout the Second War. The AT-6, in particular, and its successive variants, remained in service as a pilot training aircraft well past 1960.
As just a side note, many people incidentally know the answers to these questions and, just to be certain, spend hours doing on-line research to verify, validate, and firm-up an answer given here, on SE-Aviation. Some of this information is not easily derived, is sometimes traceable through anecdotal information or memory, or is discovered hidden in obscure ancillary sites and well documented blogs. Even though pinning down the particulars and validating an answer is hard work, there is still a chance that errors may be present in the answer given. The pieces of the puzzle are many and don't always fit together well. Most of the experts regarding the history and use of these planes are now gone. Not being an expert, this was nevertheless, a very interesting question to answer. Thanks for the opportunity, and the chance at discovery.