Apparently not in this case. But Greg Egan (of course it's Greg Egan) has written an entire novel about a civilization of sentient creatures inhabiting a universe with a (+,+,-,-) metric – time is still one-dimensional in their universe, but one of the spatial dimensions is hyperbolic: https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html
And in case anyone is new to Greg Egan, there's also the Orthogonal series (starting with The Clockwork Rocket) where the metric is (+,+,+,+) - the "time" dimension is just like the spatial dimensions. Pretty cool read with a bit of physics background!
