Speedometer (unit iteself)

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So my speedometer has a bouncing issue. Its not wild but it bounces back and forth between about 1-2 miles below or above the speed im actually driving. My speedometer also seems off by about 5 MPH however I havent changed from the stock wheels so I shouldnt have any problems with that. I bought a new speedometer cable and installed it, took it for a drive, and it seems like it may have worsened a bit. Now I know I should probally go out and re-lube the cable itself because god only knows the effort the factory put into lubing it esp since it is aftermarket brand, but I also want to take a look at the speedometer unit itself.

Additional Info: The speedometer does not make any scratching noises or anything out of the normal.

This brings me to the questions...

1. Should I be looking at anything on the transmission end of the cable? or is the only component that needs to be inspected in the instrument cluster?

2. What exactly should I be looking for once I find the speedometer unit itself? I was reading another person's post from a year or 2 ago and it said that they may need to lubricate the speedometer unit itself... If so, Where do I put the lubricant and should I be looking for anything else specific which may be related.

3. Is the white lithium grease I see mentioned in many posts be safe for the unit itself?

Thanks in advance!