Say an American army near Switzerland wants to go around the Siegfried Line. What would happen if they went through Switzerland and what would that border even look like? Other examples of this type of scenario would be really cool to hear.
Depending on what the neutral country's approach to neutrality is the border will look vastly different. Since you specifically mentioned Switzerland I will go a little into that.
In the mid thirties Switzerland's military realised that war at its borders within the next few years will be a very likely scenario and started to rebuild the army which had been shrinked since the first world war.
This included ramping up domestic military supplies production(from Oerlikon cannons to Kern binoculars), importing what couldn't be designed within reasonable time-frame(namely airplanes, fighters came from Messerschmitt and Morane Saulnier, transporters from Junkers(fun fact; they still fly today from Dübendorf)) and especially the fortifications of the border regions and the passes crossing the alps.
The last point is what is especially relevant to your question since Switzerland built a network of bunkers and fortresses along its borders. These fortifications had two main purposes
sheltering the troops from artillery and aerial bombardment
to disrupt the enemies advance with concentrated fire from artillery bunkers
This led to chains of small pillboxes being built, allowing to give each other covering fire, with additional entrenchments where needed. Major traffic axis where further covered with artillery fortresses to deny the enemy an undisturbed build up of forces. Prime examples for this are the three fortresses which made up the majority of the reduit(Martigny, Gotthard and Sargans) but also Reuenthal which covered the bridges between Waldshut and Germany or the fortifications south of Basel belong into this category.
But to answer your question what it would have looked like if one approached the Swiss border between 1939-45:
lots and lots of barbed wire along the border.
right behind that would be a footpath which would be used by patrols constantly yet irregularly
around every 800-1000m there would have been(in fact most are still) a bunker. Some were simple sentries, others were designed to serve as mg-nests others still had anti tank guns. Most were well hidden but one can only hide a bunker big enough for a squad or even platoon to a certain degree
if you were near an important street or railway line into Switzerland and new where to look you could see some fortress howitzers 5-20km away from the border.
However chances are that you would have been caught anyway and court martialed as a possible spy, which wasn't fun at all.