Can mailbox rental be a tax write off if its related to employment to show residency?

[MichaelDC]

Yes. To be deductible, a business expense must be both ordinary and necessary. So, if your mailbox rental is ordinary (common and accepted in your trade or business) and necessary (helpful and appropriate for your trade or business) you can claim it. 

An expense does not have to be indispensable to be considered necessary.