"Capitol Hill" is a proper noun as a name for both the area where the US Capitol building sits as well as a residential district. Of course these should be capitalized when used as proper nouns.
But also, in news and politics, people often use "Capitol Hill" as an informal nickname meaning "members of Congress" or areas including nearby congressional buildings that may not technically sit atop Capitol Hill, but be related to the work or culture of the Capitol. What about that?
English has some rules for "always" capitalizing words, three examples being: "I" (myself), "English", and "Indian". These words should always be capitalized.
So, is "Capitol Hill"—in reference to anything Washington, DC -related—also among words that should always be capitalized? Or, if not, what is an example of when not to?
Resources that use the term, but do not answer this question specifically: