$24k is the cap. Lets say your school is $30k. The first semester takes away about 4 months and pays for the first 15k (since 30k is for the year in this example, then 15k per semester). IF you enroll with the GI Bill in the spring, it will will cover up to 24k, so 24 - the 15k already used = 9k. The spring semester will leave you having to pay $6k. IF you do not choose to enroll with the GI Bill in the spring, in this example, you'd have to pay the whole $15k that remains. By enrolling, even though there will be some tuition left to be paid, you will still receive the book stipend and BAH. If you choose to not enroll with the GI Bill for the semester, you don't receive anything.
Even though there is a cap, and thus the whole tuition is not being pay, you're still going to be enrolled full time, so for the whole year - fall and spring, yes, the full 8 months will be utilized.
IF your school is lets say $50k, then the $24k is utilized all in the first semester (which is what it seems you typed if I didn't misread it) - in which you'd pay out of pocket $1k. IF you use the GI Bill the spring semester, you will receive the book stipend and BAH, but the cap would have already been hit, and thus no tuition would be paid. You will still lose months of benefits.
^If this is the case, I'd recommend NOT using the GI Bill for any spring semester, assuming each fall utilizes the full (or close to it) amount of tuition coverage. Living expenses for 4 months is relatively small, especially if you'd end up taking out loans for the tuition anyway. If you have scholarships to cover the tuition, or more, then great because you wouldn't have to take out as much.
By doing this, you'd also save quite a bit of time to utilize for med school with less debt than most of your counterparts, and no debt for the first 1-3 years of med school.
Hope this helps.