It’s tellig that the first involves an archaic word no longer in use. And in my pronunciation (coastal California) the second pair differ in the vowel not the consonant. I pronounce them both as in “thy”.
"either" can be pronounced two ways in the first vowel, "ee" (like "eek!") or "eye" (like "eyeball"). Same as "neither". To compare with "ether" I'm assuming the first.
But "ether" can only be pronounced with unvoiced "th". If you pronounce it voiced, that would be very unusual. Are you sure? Check out:
- "thy" and "thigh"
- "either" and "ether"