As I mentioned on IRC, I think checkboxes might be easiest and most straight forward.
So something like this:

 ________/\__________
|                     |
|                     |
|                     |
|_____________________|
|                     |
|                     |
|                     |
|_____________________|
|                     |
| [✓] nameoflayer [x] |
| [✓] nameoflayer [x] |
| [ ] nameoflayer [x] |
| [ ] nameoflayer [x] |
| (  Load Map Layer ) |
|_____________________|

Open question from IRC:
<jonasdn> andreasn: hashem should tge default action of arow be toggle show or go to layer?

Created attachment 319676 [details]
eye icon

I've gone over this in my head on and off the last couple of days, and I think my conclusion so far is that the checkboxes is a dead end, since labels of checkboxes always acts on the checkboxes.
I've added the eye instead. Lets use that as originally planned. It would go to the very left. It will also need an off state.

Created attachment 319746 [details]
visibility off icon

Created attachment 320023 [details]
Cast of using the eye

So it looks like this, what do you think? There seem to be a rendering bug with the eye though? It looks fine in firefox for me, but renders like that in Maps.

Question should the button be circular?

(In reply to Jonas Danielsson from comment #6)
> Created attachment 320023 [details]
> Cast of using the eye
> 
> So it looks like this, what do you think? There seem to be a rendering bug
> with the eye though? It looks fine in firefox for me, but renders like that
> in Maps.

It might be due to path vs objects. I can get you a new image that tries to fix that.

> 
> Question should the button be circular?

I think it looks out of place circular. I filed a bug about the close icon being circular recently, but I forgot the number.

Created attachment 320024 [details] [review]
Add a way to toggle visibility of a shape layer

Add an eye shaped button that toggles the visiblity of a
shape layer in the layers popover.

Created attachment 320025 [details] [review]
Add a way to toggle visibility of a shape layer

Add an eye shaped button that toggles the visiblity of a
shape layer in the layers popover.

Created attachment 320046 [details]
layer-visible

Updated icon to fix the gray fill issue

Created attachment 320047 [details]
layber-not-visible

Fixes the gray fill issue

These two icons above should fix the issue

Attachment 320025 [details] pushed as e1ac6f7 - Add a way to toggle visibility of a shape layer