In this example, the form "become" is the simple present form. This is also called the present indefinite form. It is simple in construction, but far from simple in use or interpretation. We use the indefinite aspect when we intend some semantic aspect other than the continuous or the perfect.
The reason that other respondents think that this sounds incomplete is that they expect the context to provide some clue as to the semantic aspect -- do they become red habitually, conditionally, periodically, or what? This ambiguity leads English speakers to use the present continuous to express the immediate present: "Your eyes are becoming red." We also tend to use adverbial markers to indicate other semantic aspect, such as: "Your eyes often become red."
- Your eyes are become red.
There are dead dialects of English for which this is a perfectly natural form. We rarely use it today, unless we're quoting an old text or otherwise trying to sound old-fashioned. In English grammar, the technical term "perfect" does not mean "flawless" and it does not mean "complete". Rather, it means "having a relevant result". In at least some of those dead dialects, using a form of "to be" to form a finite perfect verb emphasises the relevant result. In contrast, using a form of "to have" would emphasise the process that leads to the relevant result.
- Your eyes have become red.
In those dead dialects which I have mentioned, this could be the style of the perfect present construction which emphasizes the process over the result. In the vast majority of contemporary dialects, this is the only acceptable form of the present perfect construction, leaving the distinction between action and result moot.
In either case, there is a result from an action That result has a present-tense relevance. No matter when or how the action started, no matter when or how or whether the action ended, that action caused something that is relevant now. And, that relevance is, lo, the present color of your eyes.