pronouns - The all too frequent conundrum involving "who" and "whom"

Sir Reginald Wingate, a British general, is said to have described the Bedouin as “an untrained rabble, most of whom have never fired a rifle.”

Should it not have been "who" instead of "whom" in that sentence fragment?

Google search for "most of who have" returns about 2,70,00,000 results. While a similar search for "most of whom have" returns about About 70,20,000 results. I understand though, from Laurel, that a more reliable approach would be to either consult the Corpus of Contemporary American English or Google Ngram Viewer.

The problem with the sentence fragment is that it does not sound right substituting "who"/"whom" with "he"/"him".

Answer

Instead of using Google search to find frequencies (which is always laughably inaccurate), you can use a tool like the BYU corpora. I used the Corpus of Contemporary American English and searched for most of who* have (where who* matches words that start with "who", including "who" itself). The results are clear: there are 108 hits for "most of whom have" and none for anything else. Google NGrams gives similar results.

For this sentence it sounds at least slightly odd either way to "substitute he and him for who and whom" to figure it out (as moioci suggests). Instead, you can substitute they and them for who and whom (the same method, but with plurals):

...most of they/them have never fired a rifle.

In this sentence, only "them" sounds right.