It is blowing out the exhaust or intake up through the carb?
There is a huge difference in reasons. I thought you indicated up through the carb, rather than popping out the exhaust. Which is it doing? Through the carb or out the pipe?
As for vacuum lines, it pretty much doesn't matter where you get the vacuum from in an old 60's
stang.
They don't use delayed vacuum, just straight manifold vacuum. So any hole in the intake that is near the plenum will provide proper vacuum. Since there is no air or exhaust passing into the intake on a 60's
stang, the size of the hoses won't matter much either. The vacuum doesn't flow, it just sucks and moves parts.
The vacuum to the distributor pulls the plate the points are on pulls forward to advance the spark. I think it is about 20 degrees, you should look in a book to be sure. At high vacuum (low pressure) the cylinders aren't fully filled and the engine runs better (higher efficiency) with additional advance.
When you open the throttle the manifold pressure increases and the timing retards. This prevents spark knock and lugging with open throttle at low speeds by pulling the timing back when the vacuum goes away.
As the engine revs more, some weights will start dialing in more advance. This is to correct for delay in the burn at higher engine speeds and make more power at high RPM.
By not having vacuum lines you lost the low speed idle smoothness and some fuel efficiency at very light throttle. It will not cause backfiring or loss of higher RPM or wide open throttle problems unless you cranked the timing way off.
Plug a line from the distributor to any open manifold port near the plenum of the manifold and you will be fine. No need to worry. You should see the engine speed up at idle when it is connected and be able to use less throttle when cruising at constant speeds with the vacuum advance connected.
I think you have more issues than that though. You need to beg borrow or steal a dwell meter and timing light if you have a old
stang.
I was GM and an engineering supervisor at a company that manufactured dwell, timing and other test equipment. We made almost everything Sears and Snap on and others sold, but we went out of that business when electronic ignitions and foreign imports took over. :-) I hope someone still sells the stuff.
Tom