IF you really want to go square taper - NOTE, I would not - you are going to need some tools, the first of which is a caliper - I use a Harbor Freight digital caliper, often on sale for about $10- - to measure what you have.

Confirm that the cups are not threaded into the BB shell - early '80's bikes with 3 piece style cranks and Shimano's FFS have cups that are threaded into a standard 68mm x 1.375" BB shell. If they are threaded the threads will be visible inside the cups. Your pictures are not high enough resolution for me to see.

If the cups are not threaded, knock the cups out of the frame. Confirm that the ID of the BB shell is around 1.324", in which case you are almost home, because you can use a Sunlite Repair BB like this one: Sunlite Bottom Bracket Set 68 x 127.5 Sqar Thrdls F/Repair
You need to choose your crankset, then choose the BB with a compatible axle length.

If the ID of the BB shell is less than 1.324" and the wall thickness is sufficient, you could have the house reamed out. If it is less than 1.375 (and probably 1.380"), you can probably use the Sunlite BB.