Are you saying it's just the gauge that needs to be sealed, or the whole binnacle? Just wondering cause I have a home made dash and the gauges are open at the back.

The inside of the gauges are the problem, the outside shouldn't be upset by a breeze.
Its the seal around the glass which is the real source of the problem as air is blown through by the pressure difference between the engine bay and the cabin. If you listen carefully when it is happening, it really hisses through.

_________________
SooperDooperMiniCooperExpertEngineering

All garage work involves equal measures of enthusiasm, ingenuity and a fair degree of irresponsibility.

You are correct on sealing the two calibrating holes at the back to protect the bimetal strip.Do as the maker intended.The problem experienced in this post is something i have experienced many times over the years with a mini and results from the big hole in the firewall that is not always covered adequately.Do not seal the gauge completely particularly during winter as you will not be able to read the gauge for the fog.This applies to bimetal,semi conductor and cross coil.There are normally two fine holes top and bottom of the case and dial of Smiths Gauges to clear the fog.The solid state regulator is a nice idea, the Smiths one is available for a reasonable retail price in Australia which is a lot less than the effort to make one yourself and looks exactly like the original from the outside.That said the bimetal regulator works fine provided it is kept earthed adequately over its life which is now is pushing 47 years given it was introduced in a mini in september 1964.