Looks to me some wires are going bad. You'll need some troubleshooting and frequent probing at back of gauge. I recommend until you get this solved to remove the black gauge bezel and leave it off until you get this fixed.
To rule out power issues, do you see the CEL or brake light flickering during bulb check with handbrake up?
Speedo jumping means it's picking up spurious pulses or losing pulses. Fuel gauge going E means it sensed increased resistance (or an open). So you'll need to check for possible opens in a few wires.
First some terminology to make my explanation easier. The gauge has 4 plugs on the back. Brown is A, white is B, blue is C, gray is D. Pin 1 is leftmost pin looking at plug side - or maybe even stamped right on the plug. I'll say C1 is the pin 1 of plug C for example.
Speedo input is C10. Fuel gauge sender is D9. D2 is key "ON" power. Ground is B15.
Fuel gauge wires end up with the black plug with two big terminals by the driver's door kick panel. Match wire color and probe for open. Try wiggle them some or point a hairdryer somewhere close , seeing the problem doesn't show up until after 10-20 mins of driving.
The other end of speedo wires is at IG2, the blue plug with teensy pins. To get at it you need to pull of the lower console bezel around storage cubby/box and cup holder, then remove the cubby/box itself. Yeah it's a lot of work.

Again match wire color on both ends and probe the male end.
Good luck. I know you'll need it.