TT points to the baraita in Sanhedrin on “lo saguru” (verified via earlier TT extracts).
לא תגורו מפני איש — תניא: שנים שבאו לדין, אחד רך ואחד קשה, ושמעת דבריהם ואתה יודע להיכן הדין נוטה, מניין שאי אתה יכול לומר להם איני נזקק לכם? תלמוד לומר לא תגורו מפני איש.
Lo saguru mipenei ish — tanya: shenayim sheba’u ledin, echad rach ve’echad kasheh, veshamata divreihem ve’atah yodea leheichan hadin noteh, minayin she’ein atah yachol lomar lahem “eini nizkak lachem”? Talmud lomar “lo saguru mipenei ish.”
“You shall not fear any man” — it was taught: If two come to judgment, one soft and one hard, and you have heard their words and know where the judgment leans, whence do you learn that you may not say to them “I will not deal with you”? From the verse “You shall not fear any man.”
Custom — procedural timing of the prohibition against fear.
After a judge has heard the parties and knows where the law leans, he may not refuse to decide out of fear of either litigant.