No idea of the meaning, but similarly shaped and linked "rings" can be seen at other sites with glyphs attributed to the Hohokam culture. Many of these "rings" are more angular in appearance (as can be seen in one of your two examples) than "ring" shaped.
This motif can be seen at both White Tanks and the Deer Valley Petroglyph Preserve north of Phoenix. The "strand" is often oriented vertically on the rockface and sometimes appears with multiple vertically oriented strands arranged in a horizontal row. It could be interpreted as a numbering methodology.
Something is not right. This message is just to keep things from messing up down the road