Actually, I may be mistaken, I don’t think they had C-3PO blinking in the 80’s series, it was probably the animated special in The Star Wars Holiday Special (you know, the one where Boba Fett originates from) I was thinking of. Either way, he does blink in a vintage cartoon, worse yet, the Holiday Special is still canonical.
Edit: Okay, let me re-revisit this… Apparently animated C-3PO can’t help but blink, whichever version. I checked the 80’s cartoon and he does blink, but not in the extremely weird and creepy method he does in the Holiday Special. That version of blinking is really, different.