Sister's back bench seat (not the backrest, the seat) has 2 big tears in vinyl. Foam is still good. She has kids that ride in back 5 days a week. She knows she has to get it recovered, but it will be a couple weeks till she can.

What is the best short term solution? Do they make something with the same idea as a dash cap? Like a seat size piece of flexible vinyl that covers the top of seat and can be glued to existing vinyl?

Yep, contact cement both surfaces and glue a vinyl patch over the tear.

Same make and model from an auto wreckers will be WAY cheaper than any repair job.

For a couple of weeks, clean with alcohol and high end duct tape should hold. After that a seat cover is a good option if available. The JY is a good idea also.

The local junk yards in Tacoma either rarely have old cars or they want an arm and leg for even small parts. I'm really liking the idea of glueing on a piece of vinyl where would I buy about a 5' by 3' piece of similar thin vinyl from?

I have stitched vinyl on, but any glue is going to be iffy.

If we were in Seattle, I would go to Pacific Iron & Metal on 4th Ave S....if it is still there, but any of the large fabric stores have bolts of fabric including Naugahyde. I reupholstered my Kawasaki H2-750 seat with some brown Naugahyde and it was easy. Hog rings and hog ring pliers will do the job

This is the first hint of age. You haven't even told us what GM model it is yet.

I think it's a 77 Oldsmobile

Short term, you say? Throw a bed blanket on the seat cushion. Free.

Duct tape it and throw a cheap seat cover over top. Problem solved.

For what it's worth, last time I had a seat repaired I pull the upholstery off, took it to an upholstery shop and they replaced damaged sections on two bucket seat backs for $100 total.