The answer depends entirely upon how the bike is being stored and the climate you’re in.
Short engine idles weekly are actually more detrimental than letting the bike sit. Managing the stored state of the fuel is important, so take care and treat a full tank and let it be. Better to let a tank be fully topped off to reduce the evaporation area and prevent the underside of the tank top from becoming rusted. Conversely, store it near dead empty and then there’s less fuel to evaporate. Your choice.
As for short engine idles, you’re building condensation in the motor and exhaust that unless the motor (remember it’s air cooled) comes fully up to temp, that condensation lingers in the down pipes and oil tank when you kill the motor. Riding the bike for several miles normally brings the oil up to temp, the exhaust gases hot enough to evaporate the condensation, etc.
Your oil light should only come on when the key is ON, before the engine starts. Once running, the light should not be on as it’s an indication of low oil pressure.
If the bike is stored in garage, reasonably temperature controlled, I’d treat the fuel, change the oil before I store it, and then remove the battery altogether. Set the battery aside and wipe the bike down with a mist of WD-40 or something to help stave off any rust or dust.
Everyone has their own protocols for storage, but the principles above are universally true. Do what you feel makes you comfortable as long as you understand what is happening while you’re doing it.
