Perhaps from the base of sharar in the sense of that of saruq; red ochre (from its piercing color) -- vermillion.
see HEBREW sharar
see HEBREW saruq
H8350. shasher
[שָׁשֵׁר] noun [masculine] red colour, vermilion (etymology unknown); — vermilion, formerly gained from kermes insect (vermiculus): בַּשָּׁשַׁ֑ר מָשׁוֺחַ Jeremiah 22:14 (ᵐ5μίλτος, red ochre; ᵑ7 sinopis [from city Sinopis, whence the colour came PlinNH xxxv. [6] 13], compare ThatcherDB COLOURS CanneyEB1D.); בַּשָּׁשַׁ֑ר חֲקֻקִים Ezekiel 23:14.
[שָׁת], I. שֵׁת see שׁית.
II. שֵׁת see שֵׁאת below I. [שׁאה].
III. שֵׁת see II. שׁתה.