You must do so yourself.
Open a web browser window in “incognito”/“privacy” mode.
log into plex.tv with the credentials of your account #2.
go to https://app.plex.tv/desktop/#!/settings/account
Make double sure that you are in account #2.
Delete this account.
Close the web browser window.
Now you better delete the cookies of the domain plex.tv and the browser cache to purge any residual data of account #2 from your browser.
Now you must wait for 1 month.
(no, there is no way to shorten or avoid this)