我觉得应该在whether前加上that更好.
You should think it clearly （that）whether he is eligible for the job.
因为你要考虑清楚的事情是他是否胜任工作,think后面it作宾语,但是it指代的是whether he is eligible for the job.,所以应该在这句话前加上that,用以引导这个句子.