Found a garden gadget that works well for my situation, as I do not have an external spigot to run irrigation off of. This is a little solar panel with battery that runs a pump for timed drip irrigation (picture attached).
I have been very impressed with the unit, and see the benefit of having barrel reservoirs in my garden. Instead of just having water barrels, I realized that I could grow hydroponic outdoors with this easy method that I saw.
Essentially, he uses a pool noodle cut in half to float plants in a Rubbermaid tub. Cutting slits allows the plants to be slid in. It is quite the clever use. This will give some cover to the water, so that it doesn't evaporate too rapidly, and utilizes the space as grow space (instead of just water).
One concern is aeration, but I might just have one drip line feed back into the tub. If I can get it to drip into the water, it should aerate it slightly. Filling up the reservoir daily should also help aerate it.
Here is the YouTube short where he shows his method
https://youtube.com/shorts/ufC3Ex7UCy4?si=59K-mT_UTQhUbG41