We have been living in Fla for the last four years solely.
This year we purchased a home in the Ga mtns. For our second
Home. We had to get a Ga drivers license in order to purchase
A tag for the auto we'll be leaving here. We still have Fla tags
That will be purchased on Fla only license. We will be spending
Most of our time in Fla and filing taxes through Fla. My concern
Is will we be liable for Ga income taxes.

No, you are not liable for GA income taxes UNLESS you live in the state for six months or more OR unless you earn income while in Georgia.