How long to wait after removing thermal paste with alcohol?

Not very long. But since you are only using 50% alcohol use a damp lint free cloth to wipe off any residue, then take a dry lint free cloth to wipe. Let it sit for a few minutes for any residual moisture to evaporate and you are good to go.

I've already removed everything and sort of went over everything again with a Q-tip. It's been sitting there for like 10 minutes. Can I apply the thermal paste now or wait a little longer?

You can apply now.

You don't need much thermal paste, just something like a large grain of rice or a small pea will be fine.

Alcohol has a low boiling point and thus evaporates much more rapidly than water. If its a thin enough film of moisture you can literally watch it vanish in just a few seconds. It shouldn't take more than a minute or two at the most.  

Typically, you are cleaning thermal paste off the heat spreader on to of the actual CPU. You don't need to use much alcohol, just enough to wet the cloth.

Personally, I like to use the same microfiber cloths I use to clean my monitors. Just make sure you use a clean one. Be thorough, but not overzealous, when you wipe off the old TIM.

You can reapply the new TIM as soon as the heat spreader surface is dry. Alcohol is better than water in this application since it evaporates very quickly.

It doesn't take long and I would say 10 minutes is more than enough time. Like someone said you can usually see the rubbing alcohol evaporate. I usually only wait a few minutes before applying the new thermal paste.

Just to add to this, in theory alcohol is also non-electrolytic (will not conduct electricity), making it much safer than water for electronics. That doesn't mean to be careless with it, of course; don't trust it to be that pure. But anyway, that + its quick evaporation is why its ideal for this.

your talking in the order of seconds if you just wiped it on. the alcohol will evaporate pretty much as soon as you have lifted your hand off to give it another wipe...

1s you have cleaned the surface just wipe with a dry lint free cloth and yout ready to apply the new paste.

I always use 99% and it's nearly instant. 2 Minutes max.