I don't have to report the sale of a second home that was previously a rental property if there was no gain correct?

The IRS doesn't know there was no gain until you've reported the sale on the tax return.  If a 1099-S was issued, its best to include it, otherwise IRS has only seen the sales price, and will expect that to be included on the tax return.

No ... you MUST report the sale no matter what the bottom line is because the IRS got the same 1099-S form from the closing company that you did and will expect the sale on the return.  And since it was a rental property at one point you must recapture the depreciation so you may have a gain after all. 

Ahh, I read past the part about being a previous rental.  Probably some previous depreciation that needs to be included in the transaction.