Years ago I studied this in some detail (in regard to what you could run a Gnome 1400 on in awkward circumstances).
Mostly, gas turbines will actually run on just about any hydrocarbon that will go though the fuel pump. The difficulties are associated with:
getting them to light up
getting them to stay in temperature limits
getting them to stay lubricated.
There are other problems with hot and high (especially high - vapour pressures and all that).
If your engine has an automatic temperature limiter that actually works at a non-catastrophic setting, running it on petrol shouldn't cause too many problems in the short tem - ie it won't burn out and it won't flame out. What damage you are doing medium term is a different question.
Diesel has the opposite problem. Once you have it lit it should be fine. But it doesn't light as easily as kero, not that there is much between them.
If your aircraft has two tanks, the obvious advice is to put the emergency fuel (and it should only ever be that) in one tank, use the other one for start / t-o / landing / and run on the funny stuff in the cruise only, and if the situation will allow, on one engine only (you are flying a twin doing this kinda stuff, yes?)
And as has already been hinted, the sort of emergency this applies to is where somebody (you?) is definitely going to die if you don't. This is not for the normal worrying-about-regulations situation.
Iain
Still unemployed