That is a col gauge, temp and pressure.
How often do you expect to shut down on an overheat condition? Ideally, yes, you would want to cut the output power, but most every small generator I have ever seen or worked with has shut down on it's own at some point(run out of fuel, oil, fouled plugs, ect). This should be a VERY rare occurence, it will only happen if something else in the system goes drastically wrong. Most of the small installed gensets I have seen have low oil shutdowns, but no provision to open the output breaker. If you are not taking other precautions to protect vital electronics, then you are making a mistake making your own power, or even using commercial power for that mater:). the brownout during winddown isn't going to be that long, and will be steadilly decreasing at a fairly rapid rate. It could possibly deplete the reserve magnetism in the rotor, but I have never had this actually happen and have inadvertently shutdown while connected on many occasions over the years. If you are wiring your own genset and don't know how to flash the field when or if necessary, perhaps you need to broaden your knowledge base.
Shunt trip breakers are readilly available, but can be expensive. A magnetic contactor could also be added to your power output and opened by the shutdown circuit for another $30-50.