Yes the needle is adjustable but I've not had one apart. I probably don't have the tools or knowledge of 'how' to properly do the work.
It may be as simple as a missing lower stop-tab for the needle to rest against, or the needle being slightly loose on the shaft.
Otherwise I take mine to a local speedometer shop for cleaning and adjustment.
You can easily do something to help check out another
part of the other function.
Check the odometer for correct distance against GPS or 5 to 10 miles worth of mile markers on the hiway.
The odometer is gear driven and usually more accurate, if the driven gear on the lower end of the
speedo cable is 'correct', along with matching gearing in the differential.
The speedometer moves based on springs & magnets and is more likely to be affected by dust buildup, lack of lubrication or something being out of adjustment.
If the odometer distances match what the GPS or mile markers indicate... the gearing is correct and the (65+ yr old ) speedometer mechanism itself needs internal attention.
If the odometer doesn't closely match a known distance, that correction would come first before trying to get a correct speedometer reading.
Example... the odometer in my '55 is 99.9% correct when checked against known distances, but the speedometer reads approx 15mph high.
So I know the gearing and input to the speedometer head is correct and the problem is something mechanical in the speedometer or its calibration & adjustment.