I did some more searching and found the University of Florida Web Site that says:

"Many recreational pond owners purchase aerators and place them on electric timers. Proper use of the timer should have the aerator turn on during the late evening (10 p.m. to midnight) and turn off after daylight (7-8 a.m.). Using an aerator is not a complete substitute for monitoring DO concentrations and an oxygen depletion event resulting in a fish kill may still occur. However, use of an aerator is recommended and will prevent many problems."
This will be my minimum run time.

“Chemical test kits are also available. These are more troublesome to run, but are accurate and do not require as great an investment by pond owners.”
This is what I buy.

"A concentration of 5 mg/L DO is recommended for optimum fish health."
This is what I test for.

Dissolved oxygen (DO) is oxygen gas (O2) that is dissolved in water. Most DO in ponds is produced during photosynthesis by aquatic plants and algae. For this reason DO increases during daylight hours, declines during the night, and is lowest just before daybreak. Dissolved oxygen concentrations below 5 mg/L may be harmful to fish.”
At dawn is when I’ll take my random test readings.

“There has been an extended period of hot cloudy weather.
There is a heavy summer wind and a rainstorm”
These weather conditions I’ll test also.