I did not owe taxes for 2018 & filed Form 4868 for 2019 recently but DID NOT pay taxes owed because I do not have the money. Would it be beneficial for me to file my tax return and pay a nominal amount in order to qualify for the second stimulus?
As of now there is no second stimulus. Congress has not passed any legislation establishing another stimulus payment. There is no way to know what a second stimulus payment might be based on if they do pass something. You will have to wait to see whether there is a second round of stimulus payments, and if so, what the qualifications are for receiving it.
Filing an extension only gives you more time to file NOT to PAY the balance due ... if your return is ready to be filed you should ASAP and send in some kind of partial payment if you can ... then the IRS will send a bill for the balance due + penalties & interest that are accruing.