Wouldn't a pair-of-points divider be very accurate once it was set, locked and handled consistently?
Wouldn't its resolution depend on the width of the points (i.e. how pointed they are).
I'm uncertain how 'resolution' applies; the blunt points get a touch-up every once in
a while, but it's the scratchmark they make that holds the real precision of
interest. Rounded tips still make a narrow line in the Dykem.
Resolution should be high, if you think all settings in the opening range
are distinct and spaced according to the mark width.
The reason to use dividers, is to achieve symmetry. Same distance, on
all the scribed arcs... That characteristic, symmetry, is the virtue of that
instrument.
I think the 'resolution' and 'precision' concepts relate to the measurement marks
(resolution comes from the multiplicity of marks, measured in bits
as the logarithm base two...) and to the dimension that separates the marks
('precision' is the temperature difference that separates adjacent marks on,
for instance, a thermometer).
After a thermometer calibration, there is accuracy (in degrees C or F)
up to the level of the precision, in that the absolute numeric temperature
is well-known after consulting the calibration (table or curve).
There is also accuracy (lesser accuracy) in an uncalibrated thermometer,
and (if you read the data sheet) sometimes you know that the ice point
or triple point are maximally accurate because the factory did calibrate there.