Not nit-picking just trying to clear up, so it's more understandable.
The above song, "Big Bow Wow" or "Boston Harbor" the line should read;

"With our ring-tail set abft the mizzen peak".

Abft - aft, after, towards the stern

Peak - outer end of the gaff boom or the upper corner of a gaff sail.

Mizzen - The after most sail on a vessel

Ringtail - a small sail set abaft a mizzen sail or a spanker(sail) usually only set in light winds.

So the ringtail is a sail that is set even father aft then the spanker or mizzen (a fore & aft sail, not a square sail) from the end of the gaff boom at the peak & from the clew or foot (bottom outer most corner of a sail) of studding boom (an extention of the mizzen or spanker boom) that's sometimes extended from the mizzen or spanker boom (lower & last boom on a vessel). Sort of like the (portable) extending or studding yard on a squre rigger used to fly a studding sail or a stun'sa'l. Hope the explantion makes sense.

"Jinny keep your ringtail warm"

Barry