QBasic, 51 bytes
IF TIMER*2MOD 2THEN?"12:00"ELSE?"--:--
Try it at Archive.org (but note that it's an infinite loop, so there's no way to exit the program besides closing/refreshing your browser).
Displays both strings on the top line of the screen. If you're using actual QBasic rather than QB64, you'll notice that the program ...
QBasic, 71 bytes
LOCATE 24-ABS(i MOD 46-23),80-ABS(i MOD 158-79)
This version loops forever, although it might break when i gets too large--I haven't tested. Also, how fast it moves depends on the hardware you use, but on the emulator at Archive.org it runs too fast to see the motion. Therefore, here's a somewhat friendlier ...