Siemon came across “Seeing my face run the gamete from shock to anger…” in soft-core porn of a pretentiously “literary” variety, then Googled and came across a surprisingly large corpus. A web search on 10 September 2005 pulled up ca. 227 pages for “run”, 323 for “runs”, 57 for “running”, and 82 for “ran”. With as yet no access to people who use the spelling GAMETE, I’ve marked this one as questionable: how do people pronounce GAMETE in this context, and do they think there’s some connection to reproductive cells?
In non-technical English, the word “gamut” is pretty much restricted to this one idiom, and most people don’t know about its etymological connection to musical scales, so it’s open to reshaping. In any case, the spelling GAMUT, with its single M and with U representing schwa, is odd, so you’d expect spelling errors, and in fact misspellings of “gamut” are fairly frequent. Here are some Google web figures for “run the ___” (as of 10 September 2005):
Vowel U preserved:
gamut (correct spelling) over a million
gamete 227 (as above)
There are two clear tendencies in the misspellings: to double the M; and to use the vowel E preferentially, I or O less preferentially, A or U least preferentially. The moderately frequent misspelling GAMETE doesn’t double the M but does use the vowel E. However, it also has a final E, which is otherwise a rare feature of the misspellings; note that GAMMETE gets no hits. I suggest that these facts indicate that writers recognize that GAMETE is the spelling for a word of English — the other misspellings are not standard spellings of English words — which is then available (despite its own oddities of spelling) for the idiom “run the ___” ‘cover a complete range or extent’.
Which is only to argue that GAMETE can be expected as an occasional misspelling of “gamut”. It doesn’t attain eggcorn status unless we can show that there are some speakers who think that the word “gamete” is somehow involved in the idiom.
See also run the gambit.