Is there a rule in received pronunciation to know whether the final /s/ of a word is voiced or voiceless?
So, eggs is /egz/ But, in the following link it is pronounced as /egs/
Pronunciation of eggs - how to pronounce eggs correctly.
Yes. Vowels are voiced sounds.
In the terms of the OP, /s/ is always unvoiced. The letter 's' may sometimes be voiced; in that case it's not /s/, it's /z/.