Capacitor in parallel with battery for high current output
Even "directly in parallel with the batteries" isn't really directly in parallel with the batteries, thanks to wiring resistances.

The capacitor should have the closest and most direct connection to the load, then this pair should be connected to the battery via wiring which gives you some control of the current drawn from the battery.

Find the maximum recommended current (Imax) from the battery, probably from its datasheet.

Calculate the voltage drop (dV = dQ/C) across the capacitor under load, where dQ = (Iload-Imax) * pulse width - or more conservatively, Iload * pulse width.

Calculate the resistance R = dV/Imax you need in the connection to the battery. This resistance limits the current from the battery to Imax when the capacitor voltage dips by dV.

And ensure the battery wiring (including any fuse) has at least that resistance.

If dV and thus R are too high to make this all work, increase capacitance C and try again.