Gmail Draft Folder

EDIT: realized from another of your posts that you've got your account set up as IMAP. Setting for storing drafts on the Gmail server will be in Mail menu > Preferences > Accounts tab > your Gmail IMAP account > Mailbox Behaviors tab.

Hope this helps...

Assuming you are accessing your Gmail account as an IMAP account, and you have Store draft messages on the server selected for the account preferences, place your mouse on your Gmail account Drafts mailbox for a second or two - under Drafts in the mailboxes drawer.

Does the yellow dialogue box that appears indicate contents stored on the server, or locally on your hard drive?

Not sure what you mean by still going to the Mail client's Drafts mailbox.

If the Mail.app indicates this mailbox or the mailbox contents are stored on the server, the contents of this mailbox are stored on the server. If not stored on the server, the yellow box would indicate stored locally on your Mac or on your Mac's hard drive. It can't be both - it is one or the other. Stored on the server, or locally on your hard drive.

I believe what you mean is a message saved as a Draft is not available in the account's Drafts mailbox when checking the account via webmail using a browser.

Try the following, open GMAIL in the mailboxes drawer to reveal the Gmail mailboxes. Select Drafts, and at the menu bar, go to Mailbox > Use This Mailbox For, and select Drafts.