Veggies don't like to be skewered. When they begin to cook, instead of turning as you would like them to, they just lay there and burn on one side. If you really want to skewer, use two skewers, side by side, then you can turn both without a problem.
Vegetables need to be basted with an oil. I use olive oil and not extra virgin unless I am looking for that particular flavor. Baste before you put veggies on the grill, during cooking and before and after each turn. Adding seasonings to the basting sauce is an excellent way to add flavor.
Cut off the top of a large onion and put a generous pat of butter on it. If the bottom isn't flat enough for the onion to sit upright, make a bed of crumpled aluminum foil.
Zucchini, summer squash, sweet peppers, bok choy, tomatoes, egg plant, fennel, celery, broccoli (steam first) are all excellent. Slice the hard stuff into strips or rounds and baste with olive oil. Try any of these for a flavorful treat:
Don't over cook.
Veggies need a little lower temp. than proper for broiling, so move them to the side.