I stooked corn sheaves as a lad. Just listen to the lyrics and it should be clear that it's a harvest song, nor a sheep shearing song.

'An gin the weather it be hot, I'll cast off my vest and coat/ And I'll count my sheaves among yon lot when we join in the toil of shearin'

'An gin the thistle it be strang, that it would hurt your milk-white hand, it's with ma hook I'll cut it down, and forget all the toils o' shearin'

Anyway, the stooks were usually topped with a corn dolly or corn mop, never heard it called a cornet. Probably should be 'when the corn was brought home/ and placed upon the mow.

I'll go back to sleep now.