I think this has been mentioned before:

IWBNI the Analogue Clock visual wasn't always at the far left of the display - if it moved from side to side a bit (slowly!), it could be left up all the time without burning in the display.

I suggested basing the position on something like Unix time modulo some value that doesn't correlate with human time concepts (hour, day, etc) so that e.g. a daily drive to work doesn't always put it in the same position.