The capacitor value is worked out from the ripple current, the lowest frequency and the allowable voltage ripple.
The capacitance you need is the
ripple current / ( freq * voltage ripple)
The frequency will be a multiple of 5000/60, but without knowing the construction of the alternator it's not possible to know what multiple. However, the frequency that you need is lowest frequency, not the highest.
However, I don't think that the problem is ripple in the conventional sense. If the charging runs at 24 A, and the generator runs at 8 A, then the current needed from the capacitor is 16 A. If you want that to run for 5 seconds at a time, between turning on at 13.4 V and turning off at 12.4 V, then the frequency is 0.2 Hz and the "ripple" would be 16 A, and the voltage ripple would be 1 V (between 12.4 V and 13.4 V)
That gives a capacitance of about 80 Farads. As most supercapacitor work at about 3 V, you need at least 5 in series, so they need to be 400 Farads each or more.
You could go for something like this:-
https://uk.farnell.com/vinatech/vec3r0-507qg/cap-500f-3v-super-cap-radial/dp/2663723
That would be lighter than a lead-acid battery, and far more suited to being charged and discharged repeatedly.
I suggest adding some balancing resistors. Here is a link which says what needs to be done:-
https://www.analog.com/en/resources...uper-capacitor-connection-for-max3888689.html