To apply for Vote By Mail, you must do a paper application.
You can either use the voter registration application – which doesn’t require postage (https://nj.gov/state/elections/assets/pdf/forms-voter-registration/68-voter-registration-english-essex.pdf) or the dedicated Vote By Mail Application – which does require postage (https://www.nj.gov/state/elections/assets/pdf/forms-vote-by-mail/vote-by-mail-english-essex.pdf).
Both applications are to be sent directly to the County Clerk.