Apache / Httpd mod_rewrite and Files directive not working - apache

Question

I'm setting up some Apache (httpd) configuration for an Apache server fronting a Tomcat server like this:
<Proxy *>
Order deny,allow
Allow from all
AllowOverride All
</Proxy>
<IfModule mod_rewrite.c>
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^(.+)\.v(\d+)\.(js|css|png|jpe?g|gif)$ $1.$3 [L]
</IfModule>
ProxyPass / http://localhost:8080/ retry=0
ProxyPassReverse / http://localhost:8080/
ProxyPreserveHost on
<Files "*.html">
Header set Cache-Control "public, max-age=900"
</Files>
I have both the rewrite module and header module installed. The mod_rewrite rule is there so that I can version my static resources e.g. style.v2.css will be transformed to style.css etc. The custom header is to avoid aggressive caching of html files by browsers.
The proxy directives pass requests onto the Tomcat server listening on port 8080. The rewrite rules is not working though. I get a 404 for style.v2.css because it's not transforming the filename to style.css.
The custom header does not get applied either, but only because the <Files> directive is not matching my html files. If I remove the <Files> directive and apply the custom header to all files, then they all get that header in the their responses.
I'm not sure how to debug this. Is there anything obviously wrong with this configuration?
I had forgotten to include RewriteEngine On to make the rewrite rule work. It does now that I've added that. The <Files> match still doesn't work, even though I am requesting html files.
Also, using:
<Files "myfile.html">
Header set Cache-Control "public, max-age=900"
</Files>
...still does not work when I make a request specifically for myfile.html. By the way, this configuration is inside <VirtualHost _default_:443>.
I've also tried putting my <Files> directive inside a <Directory> directive, but it still doesn't work:
<Directory "/var/www">
<Files "*.html">
Header set Cache-Control "public, max-age=600"
</Files>
</Directory>

Answer 1

The Files directive was apparently useless because I had no DocumentRoot setup e.g.
DocumentRoot /var/www
Once I did that the files started matching.