Born in New York in 1925, Tindall grew up in Scituate, Massachusetts and graduated from Scituate High School in 1943. He enlisted in the Navy and served on destroyers in the Pacific, where he became interested in engineering. Tindall earned a Bachelor's degree from Brown University in 1948.
On graduating, Tindall took a job at the Langley Research Center in Hampton, Virginia, which was part of the National Advisory Committee on Aeronautics, a government agency devoted to aeronautical research. Tindall worked on wind tunnel instrumentation.
Tindall's entry into the field of aerospace engineering came when he took a position working on Project Echo, an early communications satellite. He became an expert in the field of orbital mechanics, helping to determine trajectories during Project Mercury and to plan rendezvous techniques during Project Gemini.
During the Apollo program, Tindall was appointed Chief of Apollo Data Priority Coordination. In practice, Tindall's responsibilities were wide ranging. He chaired meetings between astronauts, mission controllers, design engineers, contractors, and other relevant parties, adjudicating disagreements and overseeing the details of planning mission techniques.
Tindall was known for the colloquial and entertaining tone of his memos, which were widely referred to as "Tindallgrams." One memo was simply titled "Vent bent descent, lament.