How can I create a second email account not associated with my main Apple Account?

You would need to create an entirely new Apple Account.

click here ➜ How to create a new Apple Account - Apple Support

TipToeTippy wrote:

It isn't letting me do that. To set up an Apple ID I need an email address.

Correct. You cannot set up a stand alone iCloud account. It needs to be tied to an Apple account and that requires an existing email account.

Can't use an iCloud or me address, so I try a valid gmail address. Then a message says I can't set up an account right now...

Has that gmail address been used with an Apple account previously? If so, it cannot be used again for another one.

click here ➜ If you can’t create an Apple Account or see “your account cannot be created at this time” - Apple Support

Also note that Family sharing does not share files at all.

File sharing is a separate process outside of Family Sharing.

click here ➜ Share files and folders in iCloud Drive on iCloud.com - Apple Support

The recipient still needs an Apple Account though.

You can. There's no way for Apple to know you already have an Apple account when creating a new one to be able to block it. You are providing an entirely different email address when doing this so no way for them to tie it back to an existing one at all.

Make sure the gmail account is not already tied to an existing Apple account. You cannot create another Apple account with the same email as an existing one.

Family Sharing works across Apple Accounts. Whether the Apple account is using a gmail email as their primary email address or not is not relevant.

TipToeTippy wrote:

My alternative is to do this via gmail--and I'd really prefer not to do that. Also, that makes using files in iCloud significantly more complicated.

There are certainly a lot of good reasons for wanting to avoid Gmail/Alphabet. However, I'm not sure why you think it will make using files in iCloud more complicated. What do you mean by that?

My Apple Account ID is a Gmail address. I also have a work email address and an iCloud email address. I've experienced no issues with using files in iCloud. Perhaps if you explain more what you fear would happen, someone could give advice.

If you do go the second Apple Account route, you can always use Family Sharing to connect them.

TipToeTippy wrote:

Exactly--because of sharing. Can you use apple family sharing with a gmail account?

You can use Family Sharing if you use your Gmail address to create a second Apple Account.

And example of how I use my iCloud files from my work computer (Windows). I log into iCloud (using my Apple Account) in the browser. I can then download and upload files from my work computer.

I think you might want to explain exactly what you're trying to do. Who is this second email address for? You? Or someone else? If it's for you, why do you feel that a completely separate email address is required?