There's a bug in the A1200 design which causes this, and although you should replace your caps it might still persist. The cause is sometimes the E123R or E125R resistors. You could try shorting them with a screwdriver while Workbench is running in one of these screenmodes, and see if it improves the image. Some people solve the problem by removing the culprit resistor.
Another solution is to change your palette. The flashing and blanking you're experiencing is caused by the black and white shades in your palette, as well as possibly other shades. 255,255,255 white will do it! The best way around this is to download and install
FullPalette and use
Rebel's 16 colour palette with it, making sure to lock every pen so it keeps them after a reboot. Just make sure you set your screenmode to 16 colours, you won't need more than this when using this optimised palette.
