Songs played by the band are given in alphabetical order; all are included in a list of known cowbell songs on an internet search. The full list is:
BRASSINPOCKET DANCETHENIGHTAWAY DONTFEARTHEREAPER DONTSTOPTILYOUGETENOUGH DOWNONTHECORNER DRIVEMYCAR EVILWAYS FUNKYCOLDMEDINA GOLDDUSTWOMAN GROOVEISINTHEHEART HONKYTONKWOMEN LIFESBEENGOOD LOWRIDER PLAYTHATFUNKYMUSIC WALKTHISWAY WEREANAMERICANBAND
Bruce Dickinson mentions a different letter of the Nato Phonetic Alphabet in his commentary about every song. Reordering the songs by the order of these letters produces the new list:
DANCETHENIGHTAWAY WEREANAMERICANBAND DONTSTOPTILYOUGETENOUGH LOWRIDER HONKYTONKWOMEN DRIVEMYCAR FUNKYCOLDMEDINA EVILWAYS PLAYTHATFUNKYMUSIC GROOVEISINTHEHEART WALKTHISWAY LIFESBEENGOOD BRASSINPOCKET DONTFEARTHEREAPER DOWNONTHECORNER GOLDDUSTWOMAN
The next step is to recognize that Mr. Dickinson's repeated call for "more cowbell" should focus the solver's attention on the cowbell hits in the songs. A close inspection of each song reveals that, while the cowbell strikes for each song are all in a constant rhythm, the cowbell player misses a single strike on each song (as an example, for DANCETHENIGHTAWAY, this is the 7th strike), often using a 'pump fake' where he misses the cowbell with the beater.
Indexing the reordered list of songs by the number of the missed cowbell strike gives the clue phrase "HENRY M CLARK BREED". The puzzle answer is BROWN SWISS.