First, I've checked, cleaned, and then replaced the speed sensor already.
2000 Ultra Classic EFI. The speedometer sometimes works but most of the time bounces up and down by 30 mph. The odometer stops working as well as the turn signal auto cancel when the speedo stops. The cruise control won't work (even when speedo "working")- it turns on, sets, the speedo will jump, and it turns off. What gremlin should I be chasing?

 

Put a digital voltage meter on battery posts.
Review voltage at rest, while cranking and at high idle.
Do NOT use a dash voltage gauge if your bike has one as your reference as it is not connected directly to battery.
Possible reason for speedometer problems: An over voltage situation can cause speedometer issues.
Turn signals and cruise require speedometer reference so something causing a speedometer malfunction will not allow those units to work correctly .

 

Agree with the post above. Check your battery.
When mine started failing my speedometer started acting all wonky.
After replacing it everything was fine.

 

After checking your battery as stated above, pull all your fuses one at a time, check for corrosion on each, clean as required and put a little dielectric grease on the fuse blades, just a small amount, not a glob, a little wipe of the grease is all that is necessary.

Also check all your battery cable connections and grounding points.

 

I had a 99 Sportster XLCH 1200 do the same thing, cable from the battery to ground had corroded down to a few strands in the lug covered by the heat shrink, speedo touch and go and turn signals working when they wanted to. Check those cables.

 

I had an 02 UC and had something similar. It turned out the speed sensor had chips on it. Pulled it, cleaned it and that solved my issue. Also did all the electrical checks as mentioned above.

 

If the above does not fix it, start to look for an intermittent connection (broken wire or dirty pin). The electric speedometers count pulses over time and anything that changes the pulse rate will cause erroneous readings. A connection that adds pulses by vibrating will cause a bad reading. Since the turn signals also mess up, I would start by checking all connections between the speed sensor and the TSSM.