Probably the people best able to answer would be the Longines heritage department, if you search through this forum you should find contact details to email them, and it's free!
I am not all that familiar with Longines, but I suspect it's just a "Gents Gold Longines Automatic".
Not all watches have model names. When they do, it’s written on the dial, such as « conquest », « admiral » etc.
So I agree with @JimInOz this is a watch that’s got no specific model name.
Looks gold capped or gold plated- but I cannot see if the lugs are steel colored.
If the lugs and the watch are gold color then it’s gold plated.
Solid gold would have a solid gold case back with hallmarks and engravings indicating the grade of the gold -14K or 18K or 9K.