Can either be followed up by a plural noun?

Question

Which one is correct–

Tall fences were constructed on either side of this tunnel to channel migrating deers.

or

Tall fences were constructed on either sides of this tunnel to channel migrating deers.

Answer 1

"On either sides" sounds wrong - if "either" refers to one of two possible choices, the choice should be singular. I don't believe there is ever a case where you would say "on either sides".

You can sometimes use a plural noun after "either" - for example "The people who came to the door were either police officers or firemen."

Just a side note, but in your example you say "deers", which should not be used - "deer" is the proper plural.

Answer 2

The plural appears to be very little used, but that is true only relatively to the singular, which is used an enormous lot in comparison (ref. 1, ref; 2). So, whatever your choice, it is not likely for it to sound unnatural to anyone. However, you might prefer to follow the enormous majority that uses the singular, since it might be the case, because of their great number, that their insight is better; but the number is not always a good indication.