Take it to the dealer! I know it's a PITA, but neither of your problems should be happening, and it's their job to fix it for you. It's the principle of the thing!
Besides that, you could remove the dash bezel, the guage cluster, etc., and poke around with a multimeter to find the problem, but you might screw something else up in the process. The wiring and connections are fairly delicate in there. Then Ford would have the perfect opporunity to deny fixing the original problem, claiming that it's entirely YOUR fault.
Just my .02 cents.
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"Back in the day"-Red '66 289
"Later"- Black '68 289
"Today"- White 2000 GT
Stock except K&N & Flowmasters
ET-13.952@98.87 RT-.507 60'-2.09
Son #1 - '87 GT stock
Son #2 - '89 LX 5.0 stock