for a 1/8 hp motor the static converter is superfluous.
if you were so inclined, you could easily install a 10Uf capacitor across Phase B and Phase C and send single phase power to it on phase A and B
the problem with using a phase converter on a motor smaller than intended is the capacitance for starting is too great
the motor may receive as much as 300Uf capacitance (dependent on manufacturer)
(i have used as little as 30Uf to start an unloaded 1 hp 3 phase motor- on single phase)
the starting capacitance overkill combined with the potential relay enclosed (in all but a few brands), may be very sensitive to voltage fluctuations in the primary circuit, the potential relay will open and close a set of contacts that will dump the start capacitor's charge into the start circuit
generally speaking, the motor will attempt to speed up to about 80% of the rated RPM before the potential relay opens again.
if the intended small motor sees moderate to heavy operational demand, the potential relay will most likely be called to operation many times in an hour (sometimes in a minute for very heavy loads) the constant start and stop will surely destroy the small motor and/or the static converter due to lack of heat dissipation
the work around would be to put a smaller start capacitor in the static converter (around 20 to 30Uf)
or
install a momentary switch on the 3rd leg between the static converter and the motor
the potential relay will not be able to dump its charge without the momentary switch being closed, the static converter is effectively no longer in the start circuit. the static converter lives longer and the motor is happy on light to moderate loads
heavy loads may require other means of supplemental momentary capacitance