"has become" is present perfect tense. This tense is used to express events that
1: started sometime in the past and are still continuing
For example: Mary has worked in the Susanne International School for 2 years now. This implies that Mary started working in this school 2 years back and is still working there.
2: started sometime in the past and whose effects still continue.
For example: Researchers have found the signs of life in outer space. This implies that this action was completed in the past and its effect still continues.

"had become" is past perfect tense. This tense is used to express sequencing between two related events that happened in the past time frame. Past perfect tense is used to show the earlier of the two events.
For example: Kids had taken their bath when their mother called them for breakfast.
Here "had taken" is past perfect tense
"called" is simple past tense.
Use of past perfect tense clearly shows that the action of "taking bath" was completed before the action of "calling" took place.

To identify correct verb tense, it is very essential to understand the meaning of the sentence.
As genetics researchers achieve greater success in their attempt to map the exact locations and functions of human genes, the close connection between genes and birth defects has become increasingly clear.
This sentence implies that with the action of "researchers achieving greater success in abc", the connection between xyz becomes clear".
In more simplified terms: As action A takes place, action B also takes place.
Since A is in simple present tense, B should also be in simple present tense since both actions take place together. Thus in this sentence "becomes" is the correct verb tense.

If you would like a tutorial on verb tenses, you can refer to the concept - verb tenses - I in the free preview of e-GMAT SC course. To access the free trial you will need to register on the e-GMAT.

Thanks,

Payal