The category B listed building, which dates back to 1795, is being treated with a new lime-based render, replacing the cement which is in poor condition.
The repair works started back in August and will see the defective cement-based render removed and the sandstone prepared with the alternative before being finished in breathable masonry paint.
Scaffolding has been erected around the tower as part of the works which means surrounding roads have been affected.
The works stopped for the festive period, to support drivers and local businesses during a busy shopping period in the town.
Works at Newton Tower will recommence on Monday, January 6, and the temporary traffic restrictions will be re-instated around Main Street and King Street on Sunday, January 5.
On King Street, west bound, heading towards Main Street, the lane closest to the tower will be closed. Traffic approaching Main Street will still be able to turn left and right.
On King Street, east bound heading towards the roundabout, the lane closest to the tower will be closed up to the roundabout. Traffic will be restricted to the left-hand lane.
Drivers on Main Street, with Aldi on the left, will notice the right-hand lane outside the supermarket closed. Traffic continuing on Main Street or turning right onto King Street will use the same lane.
For those approaching the tower on Main Street heading towards the river, the inside lane will be shut along with the footpath. All traffic will turn left from the middle lane onto King Street with the bus lane unaffected (buses can proceed on Main Street past the tower).
South Ayrshire Council confirmed earlier this year that the works are expected to cost £134,000.