There seems to be a relay for the dash instruments, as my 95 gti makes a click 3 seconds after turning on the ignition, and the fuel gauge jumps to position at this point. Also seems to coincide wi fuel pump priming the rail.
I suspect your relay is at fault, but dont know where it is yet as im a new owner and don't have a manual yet :O)
May be in the fuse box under the dash at drivers side but the click seems to come from behind the clocks at the abs light end, may be behind there - anyone else know better?
Hope this helps :O)