Here is the list from Gene Beggs, October 1985 magazine article, which he claims to have thoroughly tested.
Of these, he states that it doesn't work (at least for some spin modes) for the Beech T-34C, North American AT-6 and that Cessna 150. Bill Kershner confirmed that every Cessna Aerobat behaves the same when trying to recover using Beggs-Mueller - even the 152 will not recover.
They weren't certification standard tests, for example, he did not rig the control surfaces to the extremes of the tolerances most adverse for spin recovery. What CG range did he test for each aircraft? How can he guarantee it?
His book, Spins in the Pitts Special, was published later and it had another statement: "Another aircraft that will not always recover is the 180 Decathlon. This occurs in the inverted left rudder spin. I have not flown the 180 Decathlon extensively. I do not know if the 150 Decathlon also exhibits the same behaviour." Hang on, in that earlier magazine article he stated that he had thoroughly tested it? He goes on "If we could spin-test every aircraft, I am sure we would find others that will lock-in and continue spinning on their own."
An instructor and student were conducting inverted spins in a Decathlon and the Beggs-Mueller technique was being demonstrated. The student was told to bail out and survived. The instructor was killed as he didn't have enough time to get out.
Eric Mueller is quite vague - I have only seen him state that it works for all those aircraft which have a conventional (according to Eric) tail design like that of the Pitts Special. Tell that to Paul Bennet - it doesn't work for his Wolf Pitts.