I typically would use my beanie hat, just pull it down over my eyes. I often use this while traveling on buses and trains and looking to catch some shut eye. More important to sleep on the trail is often a set of ear plugs or even better multi use, head phone plugs, the kind that goes into your ear like an ear plug. It can really help cut down on the wood being chopped and helicopters flying overhead ;)
Yea when I am hiking trip if it is morning and light out I am hiking but a mid afternoon nap on the trail can be uber wunderbar!
Sometimes I just use my bandanna fold up a couple of times and pressed into my sockets to seal out the light. Thats if its clean enough to go there.
As a side note, my girlfriend and I figured out that she has much thicker eye lids than I do. No seriously, I never thought about this before but just like some people are short and some are tall I guess some have thick lids and some have thin. This came about after we moved in together, I always sleep with shades down, she is a shade up person. We stumbled upon the idea that eye lids were different thicknesses after some basic controlled experiments (she is a scientist) we concluded this was the case. Never the less we sleep with the shades up of course!