Agon was a low-grade movement assembler, mostly working with ebauches from the likes of Bettlach, Baumgartner and Ronda. Generally these were 1 jewel pin-lever movements. Movements such as these and watches using these movements made up the greater part of Swiss output up until about 1980, so bear in mind that in a vintage watch, 'Swiss Made' does not necessarily denote any kind of quality by modern standards.
Agon's big moment of glory was their joint project with Tissot to manufacture the Astrolon/Autolub all-plastic watch movement used in the Tissot Actualis and plastic-cased Tissot Synthetic. The Astrolon was a magnificent technical achievement in mainentance-free watchmaking, but sadly failed to find a market. Tissot at that time were the lowest rung of the mid-grade watches and this may have been one step too far.
I find your watch particularly interesting because it is the first time I have ever seen the Agon name applied to the dial of a watch, rather than just the movement. I've seen these plastic cases on other brands so I suspect that the case is a generic bought in by Agon to make this model. The bad news is that it is a top-loading case, so it might require the skills of a watchmaker to open it if it needs regulating. If you do find the means to open it, please post a photo as I'm curious to know what powers this watch. There are probably a few regulars on the Vintage forum who would also be interested, and might know more about the plastic case.