If a Cosigner pays all of the the Home Equity Loan monthly payments does the Primary Signatory then get to claim the tax deduction on the interest paid or does the Cosignatory get such tax deduction?

Answer 1

You cannot claim a deduction for something you did not pay.

If the primary signatory did not pay the interest, then this person does not get to deduct it.

In order to claim a non-business/non-investment deduction for interest, the person claiming the deduction must (among other things) be the legal or equitable owner of the property. Usually, the cosignor is not the legal or equitable owner of the property, hence the cosignor cannot claim an interest deduction.