For a real nasty cooling system, I use Simple Green. Dilute it, fill up your system, and ride the scooter for a while. If you can remove the thermostat and put the housing back on, with no t-stat you can flush the whole system both ways with a garden hose. Then I run distilled water through the system, reinstall the thermostat and fill with Peak concretated coolant.
Find your cooling system capacity, and fill 1/2 that amount with full strength coolant. Top it off with distilled water. After you bleed the system, top of with 50/50 strength.
https://simplegreen.com/cleaning-tips/automotive/radiator/
This is tank out of a 15 year old Morphous from Arizona with original coolant.