Vented gas cap-- ok in garage that is under the house?

Before the 1970's emission controls, people parked cars with vented gas tanks in all kinds of garages. Some of which were surely under their houses. I don't recall ever hearing of gasoline fume explosions or any other problems caused by these vent-to-atmosphere fuel systems. Why do you think this will be a "problem" in 2017, when it was not a problem in 1967?

if you are still worried, install a vent for the garage. You can put it on a timer, and cycle it once or twice daily.

Exactly.

The lower explosive limit for gasoline is 1.4%. That would mean that the air in your garage would have to be 1.4% gasoline fumes before you could have a widespread explosion. Simply put, the odds of that happening are about nil. Your garage would have to be perfectly sealed (it's not), and it would have to be hotter than hades in there to vaporize that much fuel out of your gas tank vent all at once. The fumes coming off the gasoline in your tank under normal conditions would have an incredibly difficult path to reach the LEL. I'm not saying it's 100% impossible, but, it would have to be a pretty extraordinary set of circumstances. Now, if you had a drain catch pan full of gas sitting next to your water heater that's a different situation, that could flash off pretty easily. But that would be a localized flash, it still wouldn't be a widespread explosion. And we're talking about the fuel in your tank coming out of a small cap vent, not a pan with a large surface area of fuel exposed directly to the atmosphere near a heat source.

Now, that doesn't necessarily mean that you want the fumes coming off your car hanging out in your garage for other reasons. Like the fact that they're carcinogenic, which they didn't care about in 1967. The way around that is to have a vented garage, which, btw, you probably have already because in most places its required by building code. Even more true if you already have natural gas appliances in your garage (water heater, dryer, etc.), and doubly true because your garage is attached and below your living space. Although the relevant building code depends on how old your house is and where you live too.

Not that the charcoal canister is a bad thing, it's really not. Like a PCV valve, they're actually a pretty handy thing that came out of smog controls. Adding that back into your fuel system would be a pretty easy way to eliminate any real possibility of fumes. But more than likely the biggest issue with the vented cap in your garage will be the annoyance of smelling some gasoline in close proximity to your car on really hot days. For that matter, where do you think the fuel in your carburetor fuel bowls goes? Even with a "closed" fuel system your still have fuel exposed to atmosphere if you've got a carb. And any owner of an edelbrock or carter carb can tell you those fuel bowls are dry after a few days of sitting in a hot climate. Mine always were. 3 days or more without a start up on my Challenger and you had to crank until the fuel bowls refilled before it would start, and that car has a charcoal canister.