For younger women, you might as well be a bitch in heat with a pack in pursuit, especially gringas. If you are 40 or over, it's different in that the attention is far more courteous. You will get asked out all the time because Ecuadorian men seem to have a preference for gringas. Just find out if they're married or not because that to them does not seem to interfere too much with flirting or sometimes even dating. Which in itself says just about all you need to know. ... married or not, the men here are so flirtatious.
Actually, I've been rather surprised at how many divorced people I have met here, both men and women, surprised because it sure seems rather acceptable for such a Catholic country.
I must say that, to me, the men in Ecuador are worlds more attractive than the men in other Latin American countries I've been to. Many are tall (rare in other countries) with chiseled faces thanks to indigenous ancestry. (Look at Correa) And many look like Al Pacino....
I think one thing to be aware of it that many Ecuadorian men do not have a strong level of commitment. Many cheat on their wives, and will lie if you ask if they are married. I am lucky that I found a good one, my husband has been very good to me. But I sure met a lot of bad ones first. Men who will ask for money after the first date, serial cheaters, etc. You have to be very careful about dating men here. They are very good at hiding things they don't want you to see. But if you are careful, and diligent, you can find a good one.