I have been using bungee leashes for a while, they are reasonably tangle free, cheap to make and you make them to suit the item being leashed.
eg. the basic leash
It's a bowline loop at each end. the carabiner end is a smaller loop usually, and the larger loop is for rods/handles.
eg.
I've found the bungee holds on to the EVA great if you make the loop snug for your rod, and I don't usually slide it very far down, but you can if the rod butt allows.
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