I've seen lots of those '70's 20R Toyota's do things like this. Many times is was the Catalytic Converter getting plugged up from the
running rich all the time OR somebody running too much of those old fuel additives and it plug up the Cat. Or just a plugged up exhaust from broken bits of the inside of the exhaust system.
If it is the exhaust system it coughs and wheezes cause you are going up a hill, making it work hard and it's trying to breath and it can't because it's plugged up. The backfire comes from the red hot CAT and it can't do it's job and process the unburned fuel correctly but it's so hot it will ignite and backfire out the tail pipe.
The way to check it is where the it's does it's stunt and backfire, pull over right away and look under the truck. Most of the time you can see the Cat glowing red from the heat. Yes....GLOWING. You can also test it in town with a friend helping. Just drive it till it warms up, pull over and check how much exhaust is coming out of the tailpipe. At idle it's not much. Have you friend rev up the motor and it should be a lot coming out. If it is just a little bit exhaust coming out it's a plugged up exhaust and 99% of the time it's the CAT to blame. You can also tell as if is plugged up and you are going up a hill with the windows down you hear a hiss sound coming from the truck. It will also loose power going up hills and on the freeway but both of those things happen when it gets really plugged up. The last stage of a plugged cat is the motor will start to run a bit hotter than normal and then it will blow it's head gasket from the back pressure.
You can also stop at any exhaust shop and just have them check to see if the exhaust is plugged. They just let it run and put a small hole just before the cat and see if exhaust comes out like taking a valve stem out of a tire or not.
If you want to know how much exhaust should be coming out, just do the exhaust test on any other car and see how much comes out, your truck should be about the same. OH yes....remember exhaust gases are hot, don't burn your hand. You can use a piece of paper to hold in front of the exhaust pipe to see how much it moves. Just be careful and don't blame me if you hurt yourself...I said be careful. :)