Hi iron wizard & jwq....well, i cleaned the earth points, cleaned the ABS fuse, removed & replaced the speedo & sprayed my electronic contact cleaner stuff....all to no avail, it still does it.
However, an intersting thing i noticed while testing....if i flash my lights within a second or so of the previous flash the speedo doesn't drop....it will drop with the first flash, then when i do the 2nd & subsequent flashes the speedo remains at the correct speed - until i have a delay of about 3 secs or more, then it will dip with the 1st flash again.
i never noticed it before because i never flashed the lights i just put the headlights back on after an oncoming car had passed (which is equivalent to a single flash).
So this may change the nature of the issue! Maybe its the battery - it is 6years old after all.
As for your sidelights issue....that is really weird as it almost seems like a short to earth....