How do I find an aide to take care of my mother in exchange for room and board? She needs help with light cooking and cleaning.

employment and tenant laws will NOT work in your favor especially in NY and during a pandemic.

It may not be easy to do. And your expectations of the amount of "time off" may be a factor as often this is done by students, etc. Or someone working. The other thing you need to understand is that by making it part of the contract that room and board is being granted, that makes this person a tenant, and under tenant law they are not easily removed if you don't like the job they are doing. It is not so easy as saying "You're fired" and having them have to move out. I would consider hiring help from an agency that vets its workers or a move to assisted living. Of course I don't fully know your situation.
You are also going to run into labor law problems. A person can accept a job, and come back later saying they were actually expected to work more hours, illegally, causing you a world of woe in court and sometimes not a little money.

This has been discussed many times on this forum. Legally, you may not be able to do this. A live in aide needs to be paid a salary. They have to have time off. Call your labor board and see what the law is pertaining to live in help. You become the employer so responsible for deduction of taxes and SS. And SS has to be matched by the employer. You also need a contract to protect yourself. Members of this forum have had problems with getting live ins out of the home when the client passes or needs more care.
You maybe better hiring from an agency.