I can't give you a definite guid to deal with the Swiss / Swiss made etc.. since (not only) Longines produced many watches, especially in the 30's and 40's without any kind of "swiss..." declaration.
The way I try to verify a watch is the following (maybe it helps)
1. Check the seller, look for reputations etc. (you buy the seller^^)
2. Do your reference homework and date the watch to a certain year /period / movement
3. Compare the desired watch to other watches from that period / with the same movement etc. If you don't have any books like for example "Longines Watches by John Goldberger" to compare, use the internet. Since there are many redials around you shouldn't stop looking for further references if you found only one similar watch, the more the better.
4. Try to analyze all the prints on the dial and check them for irregularities / flaws / improper lines etc.
--> to get back to the " swiss ..." declaration, if there is no such indication it alerts me and makes me look even closer)
5. Especially for longines watches: Check for brass tone dial feet (should be brass toned and not silver, I believe from the 30s to the late 40s (Theres a an interesting thread on this forum, credits especially to DirtyDozen12) link:
https://omegaforums.net/threads/beware-problem-longines-watches.41134/
6. Check the hands, if they are lumed, see if the lume aged the same way as the lume dots on the dial (just an indicator, there are exceptions where the aging of the lume on the hands is different from the lume dots on the dial)
7. If a offer seems to be too good to be true, stay away from it or be at least over-cautious
thats a rough guide how I do it; I'm by no means an expert and there are many much higher qualified watch geeks in this forum. Anyways, hope I could help a little.