Reverse Lights & Speedometer Inaccurate

#1
I have a 1993 Toyota Corolla DX with manual transmission.

Two questions here:

Recently I checked to see if the reverse lights were working, but they were NOT. So, I checked all fuses and replaced both reverse light bulbs to no avail. My question is: where is the sensor that tells the reverse lights to activate and could it be defective?

My next questions involves the speedometer. I stepped on the gas really hard one day as I was pulling out into fast-moving traffic. Ever since I did that the speedometer has been reading 14 to 15 mph faster than the speed I'm actually going. So, if I'm going 35, the speedometer usually reads 49 or 50 mph. One day I was driving down a bumpy, gravel road and it suddenly started displaying the correct speed, but the next day went back to reading 14 to 15 mph faster than my actual speed. What could be the problem and where should I look to fix it?

Thank y'all.
 
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