Most people on this forum have a relgious belief that muscle mass hampers vertical jump. It does not significantly hamper SVJ, or RVJ off of two feet. Off of one foot, the ground reaction forces are higher, therefore more multiples of your bodyweight will be absorbed into the plant leg so it's going to place much greater stress on the tibia. In a long jump or triple jump, the GRFs are even greater and you certainly don't see muscular football players triple jumping that far. Dwight Phillips, the world champion in the long jump for the past 4 years or so used to havea lot of muscle mass, huge pecs, biceps, and still LGed 28+ ft. His SVJ was probably decent, but his long jump success was primarily due to his speed, which allowed him to create greater horizontal forces rather than vertical. I.e. he didn't get up much in the LJ but pushed forward.
I used to ignore my upperbody as well two-three years ago. It is a bad idea imo as of today because it's going to create muscular imbalances. Bench pressing and doing pullups are probably the only thing you need to do and they will make your spine feel healthier. The arm swing isn't important forcewise, but for creating the right posture/form in a vertical jump. Doing pullups and a good combo of pushing work will keep you upright and maintain integrity of the spine and do not have to add much muscle mass. DOing curls and tricep extensions can actually also improve posture but will take more time out of your day and won't contribute much to VJ. For overall health though I recommend upperbody training. The effect on vertical jump once again will primarily be impoved jumping mechanics.