Hello and welcome to the forum!
Needless to say, operating with an aux battery you don't draw current away from your cart batteries. Using the 48 to 12Vdc converter, you do draw current away from the batteries.
Lights (depending on type and how many) draw between 10 and 15 amps and radio without an amplifier draws 7 to 10 amps. So run time , if you were to run both CONTINUOUSLY from an aux battery, would equal:
amp/hour rating of the battery, divided by 25 amps, multiplied by .75 (75% of usable amp/hour capacity) or as an example: 100 amp/hour divided by 25 = 4 hours times .80 (max) = 3.2 hours.
A more realistic example would be if you ran the lights 10% of the time and the radio 70% of the time: (100 amp/hour /((15 amps x 10%) + (10 amps x 70%))) x 80% = ~30 hours.
so, if you have a place to mount the battery, a 12 Vdc automatic charger, charging it every time you charged the cart would be fine. The cost of the charger and battery would end-up costing about the same as a 25Adc 48 to 12 Vdc converter.
Using the 10%/70% example above, using the 48Vdc battery string, the reduction in cart operating time would end up negligible (since the current draw at 48 Vdc would be less than 0.75 amps).
Another + of using a separate battery would be a likely reduction of motor generated static (Amplitude Modulated) interference trying to listen to the A.M. broadcasts on your radio. Enough to make listening to A.M. pleasurable? Probably not.
If your cart is a IQ cart, the RF interference (overloading the front end of the radio or "over-riding" the F.M stations signals being received) while underway (only) is bad. The aux battery would not really reduce that since the RF is "mostly" radiated to the receivers antenna. While underway in the club car (w/ the IQ) in the 4 that I have listened-to, the radio becomes a "CD player". I am trying to avoid that in my IQ, but not completed yet.
The aux battery makes sense if you don't mind the separate charging. I personally don't like the hassle!
Good luck with that decision!