Being a 3:1 ratio tach you are correct that it should work without issue as long as it has the M12x1 thread on the back of the tach.
The needle type on that gauge is like what Smiths used in the 1950s. I have seen it on older Triumphs and Hillmans. I am sorry I cannot suggest what donor speedometer might match. If you do find a matching speedometer, in all likelihood you would need to have a ratio converter made to use it with the Bugeye's gearing.
Regardless, that is a very nice and clean looking period tachometer.
EDIT: Of course, the picture you posted of the Sprite shows it with what appears to be a "stock" speedometer so I assume I was wrong... you are not looking for a matching speedometer only the origin of the tach you have? Sorry if I misunderstood your intent.
I forgot that another car that used that style of gauge needle was the Nash Metropolitan.