Tā zài zhè jiàn shì shàng shǎnshuò-qící, ràng rén huáiyí tā zài yǐnmán shénme.
He was evasive about this matter, making people suspect he was hiding something.
Tips
memory
闪烁 literally means 'to flicker, twinkle' (like a flickering candle) - the words 'flicker' rather than landing clearly. Picture answers that flash by without really illuminating anything.
usage
Always implies suspicion - the speaker is dodging because they're hiding something. Compare with 含糊其辞 (vague but not necessarily deceptive).