My speedometer isn't working properly.

try a new speedo drive sennsor on the gearbox

You are correct in thinking if the speed sensor fails the check engine light should be on, and you should experience problems with the transmission.
It sounds like just the speedo has failed.

What make and model

May be vehicle speed sensor. Any codes?

Disconnect the posative terminal then touch the terminal to the posative a few times quickly it will reset your odometer needle to above the resting pin. This happens because you moved your posative terminal and the needles spun around and sat on the wrong side of the pin.

if it worked for a short time then check the wiring around the sensor you would have moved them around changing the sensor

try this link might help you.. speedometer doesn work Google Search

about the guage, try replacing the cable that goes to the back of the sppedomoter to the transmission

speedometer works intermitently

I'm not 100% sure but your problem may be a speed sensor.  This is just a sensor that monitors how fast the tires are moving.  These are usually easy to change.  They require usually one or two bolts to be removed and an electrical plug.  But as to the location of yours, I'm not 100% sure, but I believe it mounts somewhere on the transmission (transaxle.)
Any questions, just ask!!! Please rate!!!  Thanks