the Berasit Hebrew Dictionary

שער

'seyer' typically appears in verb form where it seems to mean something to the effect or “leave” or “flee”. There is also a noun form which is used primarily in the context of the specification for the Tabernacle in the books of Exodus. In these cases the meaning appears to be “exit” or “doorway”.

Oddly, in a few instances, contextual clues point to an alternative meaning where 'seyer' seems to mean “hair”.

'seyer' is the root word of seyerim