But if I put /support/index.php, it will lead me to a forum page stating "invalid page".
This is confusing. Never mind what the screen says. What is the URL at this point? When you say "a forum page" it implies that you've ended up in the /forums/ software.
/support isn't redirecting....just giving me a "Forbidden You don't have permission to access /support/ on this server." error
Where does the 403 come from? Is it the ordinary human lockout because there's a /support/ directory but it has no named /index file? Or have you inadvertently locked yourself out for other reasons?
Unfortunately logs are not helpful about reasons for a 403; all it ever says is "request denied by server configuration". (Thanks, logs, that much I could have worked out on my own.) But you still need to start looking at your raw logs so you can see what requests are coming in and what happens to them.
If you install a pseudo-server like MAMP or WAMP you can also run a RewriteLock. But it creates a pretty big haystack, generally not all that useful.