Carol,
I'm not sure how many of the restaurants in Monterosso take reservations. I've never had any problem just showing up, although there might be a short wait until a table is available. I'm also not sure which ones will have gluten free options. Most of the Pasta will probably be wheat based. If you can find one with gluten-free pasta, Trofie al Pesto would a good dish to try. At that time of night, all the restaurants will be busy.
The two suggestions in earlier posts are excellent. Cantina di Miky is a big favourite with many on the forum (including me). Belvedere is a larger restaurant but also very busy at times. Don't be too concerned about the occasional rumbling noises there (the train tracks pass over top of the restaurant).
Another that you could try is L' Alta Marea which is part way up Via Roma in the old town. They have a small outdoor patio and more seating inside. For Panini and other lunch items, try Fast Bar which is also in the old town. Their Linkin Park Panino is one of my favourites! You might find it really busy and crowded if there's a soccer match on!
For a "splurge" you could also try Hotel Porto Roca which is at the far end of the old town (they probably take reservations). The views from there are spectacular! Another splurge is Ristorante Miky which is at the far end of the new town (operated by the same family as the Cantina). It's more "upscale", the menu is more seafood oriented, and they may also take reservations.
Buon Viaggio!
