Time of Lunch in Spain

Lunch is the most important meal of the day for Spaniards, in any region. It means you do sit down for lunch, to enjoy a first, a second and a dessert, either in a "menú del día" in a restaurant (in Bilbao, for example, this costs around 15 to 18eur per person, including half a bottle of wine pp), or at home, like many people do. In smaller places, many shops close for around 2 to 3h and activity declines a lot, it´s time to relax and enjoy a homemade meal. Madrid is a very large and cosmopolitan city, so many touristy places in the city center will be open for food and they do not close. Similar in Seville. But it will not be a "Spanish" lunch as nobody that I know eats that early and you´ll be served tapas or raciones, or eat at a franchise food chain. And then, dinner is quite small, much less important than lunch, and it´s around 9 or 10pm, depending on the family.

No problem to find food at those times if tapas, raciones or food chain places, in any case.

will there be places open at around 12-12:30pm for lunch,

Yes, Madrid and Seville are full of tourists who eat at all kinds of hours that locals may not and businesses know and thrive on that.

We were just in both of those cities in February. You will find a lot of options open during the noon hour in the tourist areas.

When I am wondering about hours of something specific, I search for restaurants on TripAdvisor and look to see what a few have for their hours open - also to check some regional dishes.

12-12:30pm

Lots of places. Don't worry.

Thank you all for the replies and advice! We booked Cathedral tickets accordingly and will have lunch in between around 12:30 or so. Planning on just wandering into places so hopefully shouldn't have any issues, especially if we are in the more touristy areas.

There will be plenty of places serving lunch at that time in that area. Depending on what time of year you are going, the issue might be more finding a table available than whether the place itself is open. I suppose it is true that many of your fellow diners will also be tourists; but, for the life of me, I cannot see why that matters.
My only advice is if you want lunch, then choose somewhere near where you leave the Alcazar and where you will go into the catedral. They are both large places and if you wander off to another side of either, then you'll have a longer walk back.

Thanks for the tip - will definitely plan to find a place on the way from the Alcazar to the Cathedral!