Copper deficiency upregulates GSH synthesis
Copper deficiency decreases the activity of cuproenzymes and causes cellular pathologies, many manifestations of which can be linked, at least in part, to defects in antioxidant defense mechanisms.
Cells respond to copper deficiency by adjusting their glutathione (GSH) levels and upregulating genes involved in GSH synthesis" (R1)
Yet another confirmation that GSH has a critical role for copper metabolism.
But also points out that GSH synthesis can be downregulated to normal once the cell gets enough copper. This could be a tricky part for people in high oxidative stress.