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Tag archive page not working

I am having a hard time dealing with the tag base page.

When I go on a tag archive, the URL is as follows :
http://example.com/blog/tag/tag1

But when I go to
http://example.com/blog/tag

I end up with a 404.

I try redirecting /blog/tag to /blog, but then I have a redirection from /blog/tag/tag1 to /blog/tag1 which is 404 as well.

I see two solutions now :

1) Create a /blog/tag archive page that would list all tags and have a link to the /blog/tag/tag1 template (favorite solution).
I know what to code inside (in php), but when I create a new page called “tag” I am unable to create a slug using a parent page (it automatically becomes /blogtag).

2) If that is not possible, to redirect /blog/tag to /blog/ but keep the /blog/tag/tag1 structure working.

Could you please help me ?

Thank you !