[sdwr]

"to either side" or "on either side" commonly means "on both sides"

"Either" has two meanings:

- verb-wise, it separates different options (you can have either X or Y)

- noun-wise, it refers to two similar groups (there was no light on either side of the bridge, or, conversely, the bridge was lit on either side)

[quuxplusone]

Indeed. "On either side the river lie / Long fields of barley and of rye" —Tennyson

[jjtheblunt]

(Native speaker) i read either in the sense of logical or, so one side alone (tegardless of which side) or both sides at once.

Interesting how varied the ohrasing can be read, though!