From one of my earlier posts #4553.
I have cleaned my tach and speedo mechanisms twice in my years of ownership not to mention having them apart for bulb changing several times and as recently as last winter while I had the cluster apart to fit LED lights. The "1300 Manual' pages 141-143 gives a good description of dis-assembly.
Both mechanisms operate by magnetic induction. You could think of this as the "Field" and "Armature" effect. The lag and sticking you are experiencing is likely due to the "armature" and inside workings being sticky from old lubricant thereby not responding adequately to the spinning cup (field). There should be no reason for the needles to stop travelling other then friction from dried-lube but check for tiny dead bugs, cob'webs or any foreign material causing a physical obstruction. For practical purposes you can not disassemble these mechanisms.
I cleaned mine with a small artists (pointed) paint brush wet with some paint-thinner/solvent. DO NOT use anything like acetone or lacquer thinner !!!!. These volatile fluids will eat plastic and dissolve the painted face plate and odometer dials. Do NOT "test" the freedom of movement by using the needles as they may be extremely brittle and may likely fall-apart. Do not touch the "hair-spring" which returns the needle to "0". The hair-spring should not require cleaning as it does not need any form of lubrication. When cleaning do your best to hold the tach and speedometer frames in a manner which allows the dirty fluids to drip away from everything else so not run onto/into other parts. With care you can spin the field (the cup driven by the cable) with your finger or with a suitable sized screw-driver inserted into the cable receiver to test the freedom of movement and effectiveness of the cleaning. If the odometer-wheels and face-plates are dirty they can be cleaned easily - albeit by a somewhat unorthodox method. Wet a "Q-tip" with your tongue and gently wipe the surfaces. As strange as this might sound - spit is an excellent cleaner and it won't ruin the painted surfaces or leave a residual film! (So don't be drinking a "Double-Double" when you do this
Do not use compressed air to dry away the residual cleaning solvent - you'll destroy the hair-spring and certainly the needle if in contact with that kind of pressure. When you're satisfied with your efforts let the assemblies air-dry for a day to evaporate any residual solvent. A single drop of light oil applied to the drive-cable (threaded) side of each mechanism is the only lube required. The gears and moving parts in the speedometer were not intended to be oiled or greased other then what was applied during their original assembly and that would have been as much for corrosion protection for shipping then to actually lubricate them. If you look closely it's easy to see where factory lube was applied and how over the years it has migrated and dried. The entire speedometer gear mechanism should run dry as there is no significant weight/load/friction on these parts (when clean) and any form of lubricant will attract dust and dirt which will quickly dry and gum-up things again. Aimlessly spraying anything ( like WD40 ) into the housing through the odometer reset hole will prove disastrous by coating everything inside with atomized oil. This will ruin the face-plates, render the hair-springs on each dial useless, and make the odometer and trip-meter wheels malfunction.
If upon a close examination you discover hair-line fractures in the pointer/indicators as I did from 34 years of U/V and age, consider this: With a clean pointed artists paint-brush (small) give each needle one light coat of clear lacquer (the aerosol-can type because it is suitably thinned). Spray some into the aerosol can lid and dip the brush-point into that. This will help hold them together for some time. Avoid the area that will come in contact with the needle "stop" pin on the face-plate or you'll risk sticking the needle to it.
This has worked very well for myself and hope it does the same for you. Others opinions and comments would be interesting and appreciated.