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Twenty four words put S first and G third, and the vowels divide the second box almost evenly.
I takes the second box in seven of the twenty four, with A and E on six each, U on three and O on two. Only vowels appear there.
SIGHT is the most common word on the page and SIGNS is close behind. SIGMA, SIGIL, SIGHS, SIGLA and SIGNA fill out the branch.
SIGHS and SIGHT differ only at the end, and SIGNA and SIGNS do the same. That pairing is the main reason a guess inside SIG does less than it looks like it should.
SUGAR is the standout from the U branch and one of the most common words on the whole page. SEGUE carries E, and SAGES and SAGER carry A.
SOGGY and SAGGY are the two entries that repeat a letter, and both end in Y. If your puzzle shows a double and a trailing Y, the page is down to a pair.
S closes seven of the twenty four, twenty nine percent, with R on four. Ruling out a plural is the biggest single cut here.
Both are very common and they differ in every box after the S. Either one splits the page well, which is rare.
A sign in music marking a point to repeat from. SEGNI is its plural and both sit in the E branch.
Yes, it runs S, U, G, A, R. People read the SU as a unit and lose track of where the G falls.