I really don't know if I want to make this suggestion, but...
Kobo devices use the first page of an epub or PDF as the cover. This can be displayed when the device is sleeping or powered off. It can be full screen with no extra text.
Now, if the knitting pattern was a one page PDF, opening and putting the device to sleep would display the pattern and use hardly any power.
For multi-page patterns, you could split the PDF into single pages and open each as needed. It would be a pain to manage, but it would work.
But, honestly, I think that turning the WiFi and light off and turning the sleep off, or setting it a lot longer, should be enough. Any of the e-ink devices should be able to sit like that for many hours. You would want to recharge when you get home, but, unless you are away from home and knitting for a lot of hours, it should work.
You can also wake a sleeping device with a magnet. Depending on the device, it might be easier to wake it that way rather than picking it up and finding the switch or closing and opening the cover. Probably not practical unless you could attach a small enough magnet to the end of the knitting needle and tap the screen with it when needed.
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