Birmingham was a very industrial city. It was center of Pen and Pencil Making in England.
We don't know what their jobs were exactly. I have researched and found that women held one of two jobs in the pencil factories.
This picture is where the women would put the two halves of the wood around the lead. This was a job done by women.
The other job they might have done, was to box the finished product, as pictured below.
The pencil making occupation was not a cottage industry, it was a factory job.