FN did make rifles for Israel in the early 50s, and they were .7.62 NATO from the start (actually a neat trick, since they predate the NATO adoption of the cartridge***). The IDF FN K98s have the IDF crest on the receiver ring.
I have never heard of an IDF converted south American Mauser, but anything is possible, Israel used any rifle they could get their hands on.
IDF 7.62 conversions are usually easy to identify, with a large 7.62 stamped on the receiver ring, a IDF proof mark (6 pointed star with a Hebrew letter inside)and 7.62 burned into the heel of the stock. The barrel usually has the date of manufacture, as well as a Hebrew markings.
There is a lot of info on the IDF Mausers here:
https://wwiiafterwwii.wordpress.com/2015/12/14/german-98k-rifle-in-israeli-service/
I have an IDF converted WW1 Gew98
that is an excellent rifle.
The Israeli Mausers came here in two batches, the first batch were imported by Armscorp, and came direct from Israel, and are generally in much better condition. Later imports by Century came from Guatemala, and spending time in the jungle clearly did them no favors.
***On edit: This may not be the case. Ball's book does not mention the caliber of the IDF FN contract rifles, but if they were originally made in 7.62 they should have Belgian proof marks on the barrel, so far this has not been the case, they all seem to have IDF markings, so they were most likely rebarreled by Israel in the late 50s,