Good catch on the car sitting for a long time. I completely missed that. I agree, the brown color was likely from rust.
I don't know how others flush a cooling system. The simple drain and refill sometimes doesn't work very well. Here is what I do. When I flush a cooling system I back flush it by
temporarily installing one of the flush kits that has a plastic Tee fitting and garden hose adapter. I usually install the Tee fitting after the cleaner has been in the motor and it's ready to be flushed out.
1. Using your choice of cleaners, after the cleaner has done its work and is ready to be flushed out. (Note that most cleaners are to be added to a system with water only and not coolant. So you may need to first drain the antifreeze than add the cleaner and refill with water only.) Remove one end of the heater hose that the Tee fitting attaches to. This is usually at the heater core end. Double check which heater hose to use for a Cleveland. For other motors it's simply the heater hose going into the intake manifold.
2. Attach the Tee to the removed end of the heater hose, then add a temporary piece of heater hose from the Tee to the heater core.
3. Carefully remove the radiator cap and drain the system through the radiator drain valve to try to catch the majority of the bad stuff.
4. Attach the garden hose to the Tee fitting. Then with the radiator cap still removed flush, flush, flush, letting the water, remaining coolant, and grime come out of the top of the radiator and hope your neighbors don't frown at the water running down the drain.
5. After flushing the system simply remove the Tee and temporary hose, and reconnect the heater hose.
6. After back flushing the system will be full of clear water. So drain it through the radiator drain valve and refill with 50/50 mix of antifreeze and water (distilled water helps slow down corrosion)
7. Last, hope all the old freeze plugs and gaskets are still good.
The only reason I like to remove the Tee fitting when finished is because back when I worked at GM dealer we had a couple of cars towed in because the plastic Tee fitting for flushing broke.
Regards,
Mike