Either usually means “one or the other’, but occasionally it can mean “both’:
Come on Monday or Tuesday. Either day is OK.
There were roses on either side of the door (i.e. on both sides).
We use a singular noun or verb with either, but plural noun with “both”, as in the example above: “on both sides”.
Has either of your parents visited you?
When “either” is followed by a noun phrase, there must be another determiner. You can say: either of the rooms, or either of my rooms, but not either of rooms.
Before a personal pronoun, either of is always used and the verb is singular:
Either of us could do it. (not: either you…)
Either of the children is capable of looking after the baby.
But in an informal style, and particularly, in negative sentences plural verbs are normally used:
I don’t think either of them are at home.
The irony and unfairness of that didn’t elude either of them. (Danielle Steel)
But either way he felt haunted for hours afterward whenever they met. (Danielle Steel)
“We’ ll see,” she said, not promising him anything either way. (Danielle Steel)
They went for long walks at night, away from the fairground, where people wouldn’t recognize either of them. (Danielle Steel)
She was twenty two years younger than he was but it didn’t bother either of them. (Danielle Steel)
Toby wouldn’t want that for either of us. (Danielle Steel)
And the woman in the pink shirt gave a victorious grin, and was patted on the back by two attractive women on either side. (Danielle Steel)
Green curtains (some sort of velvety material) were hanging down on either side of the window. (Danielle Steel)
Being Southerners, it was a source of shame to some members of the family that we had no recorded ancestors on either side of the Battle of Hastings. (Harper Lee)
I don’t want either of you bearing a grudge about this thing, no matter what happens. (Harper Lee)
Either can be used instead of “also” and “too” in negative sentences:
“I like opera.” – “I do too”.
“I don’t like opera.” – “I don’t either”.
I knew my word wouldn’t suffice, and I didn’t think his would impress her either, but I think she was feeling worse than she wanted to admit. (Danielle Steel)
He didn’t want to lie to him and he didn’t want to tell him the truth yet either. (Danielle Steel)
I don’t want that to happen either. (Danielle Steel)
And with the risk of being sent to a labor camp he didn’t want them to stay either. (Danielle Steel)
She wasn’t in the mood either. (Danielle Steel)
I’m not much of a cook either. (Danielle Steel)
“My mama won’t let me play on it either,” Rosie confessed to Nick… (Danielle Steel)
… but she couldn’t imagine him staying either, once Germany returned to normal, which they all felt sure it would one day. (Danielle Steel)
She didn’t wasn’t to wait either.
You can’t live hidden away in the country forever either. (Danielle Steel)
“He doesn’t look as though he’s trying to get a taxi, either,” I said. (Danielle Steel)
Jem had never seen snow either but he knew what it was. (Harper Lee)