I’ve written that the perspective of 1D space + 3D time is just as legitimate as the usual 3D space + 1D time. Is there an intermediate perspective of 2D space + 2D time? In a sense, Yes. This is the perspective of 2D images.
Maps are usually 2D images of space but they may represent other variables. Travel time may be represented on a map (see here) or a timetable. This is 2D time.
The motion of circular clocks are also 2D (see here). Although this is usually taken as a 1D angle, the point of a clock hand could be taken as having x and y coordinates in 2D.
The individual frames of a motion picture on film represent 2D space. Even though the camera or the action may have an implicit third dimension, the image always shows only 2D.