Although the situation you describe is not an every-day occurrence, it does happen often and we should know what to do. In fact, in two of the most recent (U.K. Albacore) Championships (Llandudno '94 and Hayling Island '97), the winner was probably decided pretty early on in the week on the "whim" of the sea breeze.

"Whim" is, of course, not the right word, for although places were won and lost as the old wind died and the new breeze filled in, the environment acted exactly as it should have. Consequently, it should have been straightforward to forecast what to do tactically.

Here is what happened:

Llandudno '94, Race 1:

The breeze had been light and fitful all race but on the final port reach the wind died virtually to nothing. The first few boats headed away from the leeward mark on a painfully slow port tack heading out towards the open sea. They expected the sea breeze to fill in from that direction. In it came, gently at first and the first 4 boats carried on out to sea up to and maybe even beyond the starboard layline. They obviously hoped that the breeze would be stronger out there. Boat 5 tacked short of the layline as soon as there was enough wind to get the helm on the side deck.

Within minutes all the boats had tacked and were spread out over quite a large area. All were soon up to hull speed. As the wind strength increased it began to veer big time. Soon the windward-most boats were reaching. Unfortunately for them, there wasn't enough wind to plane and so they had very little speed advantage over the leeward-most (still) beating boat.
The helm of this boat, realising that the new wind, having defeated the old breeze, was going to continue to veer as it increased in strength, bore away slightly to match the speed of the windward boats.

Gradually, and after quite a nerve-wracking time, it became clear that this boat was pulling ahead (the windward boats beyond the 2 Ormes were probably in a stronger adverse tide). All the way up to the finishing line, this leeward boat kept on a good solid full and by reach, whilst for the windward boats the leg became broader and broader and slower and slower.
 

Hayling Island, Race 4:

A light wind from the SW with cumulus building over the South Downs was the scene as the fleet beat out to the start. At the start itself, the Pathfinder was headed slightly on port as the wind began to drop. Looking to windward, there was clearly less wind on the left hand side of the beat.

For a while it looked good for the late starters (including the Pathfinder). The wind was still heading on port and so a good proportion of the fleet tacked right, hoping (eventually) to get the starboard lift.

It never came. Whilst these boats were still moving in the old breeze, a new wind filled in from the South - exactly where it always does at Hayling! However, because the old breeze refused to die on the right of the beat, the new breeze front took ages to track downwind.

The early starters were now virtually all on port tack, being freed and were up to hull speed. By the time the late starters had crossed to the new breeze and to the windward mark, these leaders were way beyond the gybe mark.

Then, as always happens on the South coast on a sea breeze day, the wind gradually veered and increased in strength.

So what lessons can be learnt from these 2 races?

As Llandudno proved, sailors should always tack short of the layline in a new wind, having already tacked towards the favoured side of the beat. Then, if it continues to free they will have gained truck-loads. Even if it doesn't, they won't have lost anything and if the old breeze decides to make a comeback, they are in the right place to take advantage of it.

By the way, this rule also applies in an ordinary steady sort of windbend beat - just like the ones you get for example on a sea breeze day at Looe. Then the tactic is to tack about 60% into the bend - although guessing where the 60% point is can be tricky!.

As Hayling Island proved on a sea breeze day, sailors should always use the last vestige of the old dying breeze to tack towards the sea - towards the area where the wind is dying most. That is where the battle between the old and new winds is being fought and lost - usually by the old wind.

Interestingly, this was beautifully demonstrated at the Cadet Worlds in Australia earlier this year when the morning land breeze died away to nothing. With a "wham" the sea breeze then filled in from the opposite side of the course and within seconds was up to force 4 in strength. Get left at any cost was the order of the day as the land breeze died, because once the sea breeze came in, those left hand boats could spinnaker plane into (what had been) the windward mark!

Auntie Alb