:: sparring for time until whitespace or someone like him shows up ::
And then would I need to put any php code in the html itself?
Only if you went with Option B: have a single page but generate it dynamically so it serves up different
content based on server time. In that case you'd need to set an extremely short expiration time-- an hour or so-- so users don't see the "wrong" content if they check back 12 hours later. In fact, is that the reason you want two different pages, like an "open now" page and a "closed now" page, so browsers don't cache the wrong one? It wouldn't work, though, since browser caching is based on URL, not physical file. (Server caching/expiration is based on physical file.)
I assume you've already eliminated the javascript approach, which is probably the simplest of all but doesn't help with users who have scripting turned off. (So long as you remember to check something absolute, like server time or UTC, and not the user's local time!)
would that php file, index.html and index1.html all go in the root folder?
Technically they don't have to. A DirectoryIndex file doesn't absolutely have to live in the directory that it's acting as index for, though it's certainly less complicated that way. Similarly the php can be located anywhere that a request can "see" it.
I think before you attack the "how to" you need to be absolutely certain about what you want to achieve, and why.