Yes, the 1/10 mile or km gear slips on the axle; it needs instead to be secured to the axle on which it rides. This has been discussed a fair number of times; I've done it with 2002 and 3.0CS instruments, they are largely the same. Briefly: first you have to take the instrument from the cluster, either alone or with the other instruments. Next (the hard part) you have to gently and carefully pry away the chrome trim ring. Then you can get inside the instrument and see how it works. In the end, either use a pinhead-size drop of superglue, or take out the shaft and carefully and slightly deform it where the 1/10 gear wheel rides. Reassemble and away you go!
Careful use of the Search function will bring up more detailed description and pictures, should you be the sort that does his own work. Even if you're not, possibly you can extract the instrument head from the dash and send it off for cleaning and repair.
I have a spare speedo head, marked in kph.... make offer. The tripmeter reset is damaged but it's otherwise good; you can easily transplant your reset device to a replacement instrument.
Charlie