Welcome to the forum!
I was just out in Big Bend a few weeks ago.
It sure was nice other than being sorta busy.
Here's what I'd do:
Plug that rear tire ............. and then swap it with the one from Dad's bike when he's not looking!
You're welcome & happy to help! LOL
Seriously, it depends on how much tread is remaining as to how I handle a puncture.
If it's a new tire, I take it off and install one of the plug/patch fixes that looks like a witches hat.
If it's a well worn tire, I just usually swap it our and dispose of it.
If it's somewhere in between, I will plug it and ride it until I get back home and then decide how to handle it.
I've ridden plugged tires for lots of miles. I'd recommend to invest some time & practice plugging on an old tire where you can see what's going on "inside" the tire. There's a technique where you can give the plugging tool a "twist" as you remove the tool and leave the cord plug. (I don't use buttons ..... just the rubber inpregnated cords.) Once you get a feel for doing that, it'll leave a small "wad" of the cord that will not come out under any circumstances. Once it cures it get's pretty hard. I also carry a spare container of rubber cement with me and I use it sparingly after I've reamed the hole, and I apply it to the cord to be inserted. The rubber cement cleans the reaming tool, and it lubricates the cord/insertion tool. It's like anything else ........ practice and learn. BTW, I ride quite a bit ........ and I can't afford to toss perfectly good tires just because they got a puncture.
Good luck and safe riding!