86 GT Coupe electrical - need help!

[Mark Donohoe]

I may purchase an 86 coupe with a bit of an electrical problem.  It has
the digital dash.  The middle section is not illuminated but I can see
it operating.  Hopefully it's just a bulb.  The biggest issue is what
seems to be an interruption in the electrical system that possibly
occurs when the fan kicks on.  This split second interruption causes the
dash to blank out for a second.  When it comes back on, my fuel tank
suddenly reads empty instead of 1/2 full (I had just put 6 gallons in
it) and the fuel alarm is beeping at me.  Any ideas as to what could
cause this problem?  

Thanks,
Mark